Compound and Continuous Interest
Mar 11, 2016
Compound and Continuous Interest
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111. Investigate the behavior of the functions f1(x) ! x!e x,f2(x) ! x2!ex, and f3(x) ! x3!ex as x S " and as x S #",and find any horizontal asymptotes. Generalize tofunctions of the form fn(x) ! xn!ex, where n is any positiveinteger.
112. Investigate the behavior of the functions g1(x) ! xe x,g2(x) ! x2ex, and g3(x) ! x3ex as x S " and as x S #",and find any horizontal asymptotes. Generalize to func-tions of the form gn(x) ! xnex, where n is any positiveinteger.
113. Explain why the graph of an exponential function cannotbe the graph of a polynomial function.
114. Explain why the graph of an exponential function cannotbe the graph of a rational function.
APPLICATIONS*!115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 forthe child’s education 17 years from now? Compute the answer tothe nearest dollar.
!116. FINANCE A person wishes to have $15,000 cash for a newcar 5 years from now. How much should be placed in an accountnow if the account pays 9.75% compounded weekly? Computethe answer to the nearest dollar.
117. MONEY GROWTH If you invest $5,250 in an account pay-ing 11.38% compounded continuously, how much money willbe in the account at the end of(A) 6.25 years? (B) 17 years?
118. MONEY GROWTH If you invest $7,500 in an accountpaying 8.35% compounded continuously, how much money willbe in the account at the end of(A) 5.5 years? (B) 12 years?
!119. FINANCE If $3,000 is deposited into an account earn-ing 8% compounded daily and, at the same time, $5,000 isdeposited into an account earning 5% compounded daily,will the first account be worth more than the second?If so, when?
!120. FINANCE If $4,000 is deposited into an account earning9% compounded weekly and, at the same time, $6,000 isdeposited into an account earning 7% compounded weekly,
will the first account be worth more than the second? Ifso, when?
!121. FINANCE Will an investment of $10,000 at 8.9% com-pounded daily ever be worth more at the end of any quarter thanan investment of $10,000 at 9% compounded quarterly?Explain.
!122. FINANCE A sum of $5,000 is invested at 13% com-pounded semiannually. Suppose that a second investment of$5,000 is made at interest rate r compounded daily. Both in-vestments are held for 1 year. For which values of r, to thenearest tenth of a percent, is the second investment better thanthe first? Discuss.
!123. PRESENT VALUE A promissory note will pay $30,000 atmaturity 10 years from now. How much should you pay for thenote now if the note gains value at a rate of 9% compoundedcontinuously?
!124. PRESENT VALUE A promissory note will pay $50,000 atmaturity years from now. How much should you pay for thenote now if the note gains value at a rate of 10% compoundedcontinuously?
125. MONEY GROWTH Barron’s, a national business and finan-cial weekly, published the following “Top Savings DepositYields” for -year certificate of deposit accounts:
Gill Savings 8.30% (CC)Richardson Savings and Loan 8.40% (CQ)USA Savings 8.25% (CD)
where CC represents compounded continuously, CQ com-pounded quarterly, and CD compounded daily. Compute thevalue of $1,000 invested in each account at the end of years.
126. MONEY GROWTH Refer to Problem 125. In another issueof Barron’s, 1-year certificate of deposit accounts included:
Alamo Savings 8.25% (CQ)Lamar Savings 8.05% (CC)
Compute the value of $10,000 invested in each account at theend of 1 year.
127. FINANCE Suppose $4,000 is invested at 11% compoundedweekly. How much money will be in the account in(A) year? (B) 10 years?
Compute answers to the nearest cent.
128. FINANCE Suppose $2,500 is invested at 7% compoundedquarterly. How much money will be in the account in(A) year? (B) 15 years?
Compute answers to the nearest cent.
34
12
212
212
512
S E C T I O N 5–1 Exponential Functions 469
CA
*Round monetary amounts to the nearest cent unless specifiedotherwise. In all problems involving interest that is compoundeddaily, assume a 365-day year.
bar67388_ch05_452-469 11/30/06 21:13 Page 469
111. Investigate the behavior of the functions f1(x) ! x!e x,f2(x) ! x2!ex, and f3(x) ! x3!ex as x S " and as x S #",and find any horizontal asymptotes. Generalize tofunctions of the form fn(x) ! xn!ex, where n is any positiveinteger.
112. Investigate the behavior of the functions g1(x) ! xe x,g2(x) ! x2ex, and g3(x) ! x3ex as x S " and as x S #",and find any horizontal asymptotes. Generalize to func-tions of the form gn(x) ! xnex, where n is any positiveinteger.
113. Explain why the graph of an exponential function cannotbe the graph of a polynomial function.
114. Explain why the graph of an exponential function cannotbe the graph of a rational function.
APPLICATIONS*!115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 forthe child’s education 17 years from now? Compute the answer tothe nearest dollar.
!116. FINANCE A person wishes to have $15,000 cash for a newcar 5 years from now. How much should be placed in an accountnow if the account pays 9.75% compounded weekly? Computethe answer to the nearest dollar.
117. MONEY GROWTH If you invest $5,250 in an account pay-ing 11.38% compounded continuously, how much money willbe in the account at the end of(A) 6.25 years? (B) 17 years?
118. MONEY GROWTH If you invest $7,500 in an accountpaying 8.35% compounded continuously, how much money willbe in the account at the end of(A) 5.5 years? (B) 12 years?
!119. FINANCE If $3,000 is deposited into an account earn-ing 8% compounded daily and, at the same time, $5,000 isdeposited into an account earning 5% compounded daily,will the first account be worth more than the second?If so, when?
!120. FINANCE If $4,000 is deposited into an account earning9% compounded weekly and, at the same time, $6,000 isdeposited into an account earning 7% compounded weekly,
will the first account be worth more than the second? Ifso, when?
!121. FINANCE Will an investment of $10,000 at 8.9% com-pounded daily ever be worth more at the end of any quarter thanan investment of $10,000 at 9% compounded quarterly?Explain.
!122. FINANCE A sum of $5,000 is invested at 13% com-pounded semiannually. Suppose that a second investment of$5,000 is made at interest rate r compounded daily. Both in-vestments are held for 1 year. For which values of r, to thenearest tenth of a percent, is the second investment better thanthe first? Discuss.
!123. PRESENT VALUE A promissory note will pay $30,000 atmaturity 10 years from now. How much should you pay for thenote now if the note gains value at a rate of 9% compoundedcontinuously?
!124. PRESENT VALUE A promissory note will pay $50,000 atmaturity years from now. How much should you pay for thenote now if the note gains value at a rate of 10% compoundedcontinuously?
125. MONEY GROWTH Barron’s, a national business and finan-cial weekly, published the following “Top Savings DepositYields” for -year certificate of deposit accounts:
Gill Savings 8.30% (CC)Richardson Savings and Loan 8.40% (CQ)USA Savings 8.25% (CD)
where CC represents compounded continuously, CQ com-pounded quarterly, and CD compounded daily. Compute thevalue of $1,000 invested in each account at the end of years.
126. MONEY GROWTH Refer to Problem 125. In another issueof Barron’s, 1-year certificate of deposit accounts included:
Alamo Savings 8.25% (CQ)Lamar Savings 8.05% (CC)
Compute the value of $10,000 invested in each account at theend of 1 year.
127. FINANCE Suppose $4,000 is invested at 11% compoundedweekly. How much money will be in the account in(A) year? (B) 10 years?
Compute answers to the nearest cent.
128. FINANCE Suppose $2,500 is invested at 7% compoundedquarterly. How much money will be in the account in(A) year? (B) 15 years?
Compute answers to the nearest cent.
34
12
212
212
512
S E C T I O N 5–1 Exponential Functions 469
CA
*Round monetary amounts to the nearest cent unless specifiedotherwise. In all problems involving interest that is compoundeddaily, assume a 365-day year.
bar67388_ch05_452-469 11/30/06 21:13 Page 469
111. Investigate the behavior of the functions f1(x) ! x!e x,f2(x) ! x2!ex, and f3(x) ! x3!ex as x S " and as x S #",and find any horizontal asymptotes. Generalize tofunctions of the form fn(x) ! xn!ex, where n is any positiveinteger.
112. Investigate the behavior of the functions g1(x) ! xe x,g2(x) ! x2ex, and g3(x) ! x3ex as x S " and as x S #",and find any horizontal asymptotes. Generalize to func-tions of the form gn(x) ! xnex, where n is any positiveinteger.
113. Explain why the graph of an exponential function cannotbe the graph of a polynomial function.
114. Explain why the graph of an exponential function cannotbe the graph of a rational function.
APPLICATIONS*!115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 forthe child’s education 17 years from now? Compute the answer tothe nearest dollar.
!116. FINANCE A person wishes to have $15,000 cash for a newcar 5 years from now. How much should be placed in an accountnow if the account pays 9.75% compounded weekly? Computethe answer to the nearest dollar.
117. MONEY GROWTH If you invest $5,250 in an account pay-ing 11.38% compounded continuously, how much money willbe in the account at the end of(A) 6.25 years? (B) 17 years?
118. MONEY GROWTH If you invest $7,500 in an accountpaying 8.35% compounded continuously, how much money willbe in the account at the end of(A) 5.5 years? (B) 12 years?
!119. FINANCE If $3,000 is deposited into an account earn-ing 8% compounded daily and, at the same time, $5,000 isdeposited into an account earning 5% compounded daily,will the first account be worth more than the second?If so, when?
!120. FINANCE If $4,000 is deposited into an account earning9% compounded weekly and, at the same time, $6,000 isdeposited into an account earning 7% compounded weekly,
will the first account be worth more than the second? Ifso, when?
!121. FINANCE Will an investment of $10,000 at 8.9% com-pounded daily ever be worth more at the end of any quarter thanan investment of $10,000 at 9% compounded quarterly?Explain.
!122. FINANCE A sum of $5,000 is invested at 13% com-pounded semiannually. Suppose that a second investment of$5,000 is made at interest rate r compounded daily. Both in-vestments are held for 1 year. For which values of r, to thenearest tenth of a percent, is the second investment better thanthe first? Discuss.
!123. PRESENT VALUE A promissory note will pay $30,000 atmaturity 10 years from now. How much should you pay for thenote now if the note gains value at a rate of 9% compoundedcontinuously?
!124. PRESENT VALUE A promissory note will pay $50,000 atmaturity years from now. How much should you pay for thenote now if the note gains value at a rate of 10% compoundedcontinuously?
125. MONEY GROWTH Barron’s, a national business and finan-cial weekly, published the following “Top Savings DepositYields” for -year certificate of deposit accounts:
Gill Savings 8.30% (CC)Richardson Savings and Loan 8.40% (CQ)USA Savings 8.25% (CD)
where CC represents compounded continuously, CQ com-pounded quarterly, and CD compounded daily. Compute thevalue of $1,000 invested in each account at the end of years.
126. MONEY GROWTH Refer to Problem 125. In another issueof Barron’s, 1-year certificate of deposit accounts included:
Alamo Savings 8.25% (CQ)Lamar Savings 8.05% (CC)
Compute the value of $10,000 invested in each account at theend of 1 year.
127. FINANCE Suppose $4,000 is invested at 11% compoundedweekly. How much money will be in the account in(A) year? (B) 10 years?
Compute answers to the nearest cent.
128. FINANCE Suppose $2,500 is invested at 7% compoundedquarterly. How much money will be in the account in(A) year? (B) 15 years?
Compute answers to the nearest cent.
34
12
212
212
512
S E C T I O N 5–1 Exponential Functions 469
CA
*Round monetary amounts to the nearest cent unless specifiedotherwise. In all problems involving interest that is compoundeddaily, assume a 365-day year.
bar67388_ch05_452-469 11/30/06 21:13 Page 469
111. Investigate the behavior of the functions f1(x) ! x!e x,f2(x) ! x2!ex, and f3(x) ! x3!ex as x S " and as x S #",and find any horizontal asymptotes. Generalize tofunctions of the form fn(x) ! xn!ex, where n is any positiveinteger.
112. Investigate the behavior of the functions g1(x) ! xe x,g2(x) ! x2ex, and g3(x) ! x3ex as x S " and as x S #",and find any horizontal asymptotes. Generalize to func-tions of the form gn(x) ! xnex, where n is any positiveinteger.
113. Explain why the graph of an exponential function cannotbe the graph of a polynomial function.
114. Explain why the graph of an exponential function cannotbe the graph of a rational function.
APPLICATIONS*!115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 forthe child’s education 17 years from now? Compute the answer tothe nearest dollar.
!116. FINANCE A person wishes to have $15,000 cash for a newcar 5 years from now. How much should be placed in an accountnow if the account pays 9.75% compounded weekly? Computethe answer to the nearest dollar.
117. MONEY GROWTH If you invest $5,250 in an account pay-ing 11.38% compounded continuously, how much money willbe in the account at the end of(A) 6.25 years? (B) 17 years?
118. MONEY GROWTH If you invest $7,500 in an accountpaying 8.35% compounded continuously, how much money willbe in the account at the end of(A) 5.5 years? (B) 12 years?
!119. FINANCE If $3,000 is deposited into an account earn-ing 8% compounded daily and, at the same time, $5,000 isdeposited into an account earning 5% compounded daily,will the first account be worth more than the second?If so, when?
!120. FINANCE If $4,000 is deposited into an account earning9% compounded weekly and, at the same time, $6,000 isdeposited into an account earning 7% compounded weekly,
will the first account be worth more than the second? Ifso, when?
!121. FINANCE Will an investment of $10,000 at 8.9% com-pounded daily ever be worth more at the end of any quarter thanan investment of $10,000 at 9% compounded quarterly?Explain.
!122. FINANCE A sum of $5,000 is invested at 13% com-pounded semiannually. Suppose that a second investment of$5,000 is made at interest rate r compounded daily. Both in-vestments are held for 1 year. For which values of r, to thenearest tenth of a percent, is the second investment better thanthe first? Discuss.
!123. PRESENT VALUE A promissory note will pay $30,000 atmaturity 10 years from now. How much should you pay for thenote now if the note gains value at a rate of 9% compoundedcontinuously?
!124. PRESENT VALUE A promissory note will pay $50,000 atmaturity years from now. How much should you pay for thenote now if the note gains value at a rate of 10% compoundedcontinuously?
125. MONEY GROWTH Barron’s, a national business and finan-cial weekly, published the following “Top Savings DepositYields” for -year certificate of deposit accounts:
Gill Savings 8.30% (CC)Richardson Savings and Loan 8.40% (CQ)USA Savings 8.25% (CD)
where CC represents compounded continuously, CQ com-pounded quarterly, and CD compounded daily. Compute thevalue of $1,000 invested in each account at the end of years.
126. MONEY GROWTH Refer to Problem 125. In another issueof Barron’s, 1-year certificate of deposit accounts included:
Alamo Savings 8.25% (CQ)Lamar Savings 8.05% (CC)
Compute the value of $10,000 invested in each account at theend of 1 year.
127. FINANCE Suppose $4,000 is invested at 11% compoundedweekly. How much money will be in the account in(A) year? (B) 10 years?
Compute answers to the nearest cent.
128. FINANCE Suppose $2,500 is invested at 7% compoundedquarterly. How much money will be in the account in(A) year? (B) 15 years?
Compute answers to the nearest cent.
34
12
212
212
512
S E C T I O N 5–1 Exponential Functions 469
CA
*Round monetary amounts to the nearest cent unless specifiedotherwise. In all problems involving interest that is compoundeddaily, assume a 365-day year.
bar67388_ch05_452-469 11/30/06 21:13 Page 469
111. Investigate the behavior of the functions f1(x) ! x!e x,f2(x) ! x2!ex, and f3(x) ! x3!ex as x S " and as x S #",and find any horizontal asymptotes. Generalize tofunctions of the form fn(x) ! xn!ex, where n is any positiveinteger.
112. Investigate the behavior of the functions g1(x) ! xe x,g2(x) ! x2ex, and g3(x) ! x3ex as x S " and as x S #",and find any horizontal asymptotes. Generalize to func-tions of the form gn(x) ! xnex, where n is any positiveinteger.
113. Explain why the graph of an exponential function cannotbe the graph of a polynomial function.
114. Explain why the graph of an exponential function cannotbe the graph of a rational function.
APPLICATIONS*!115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 forthe child’s education 17 years from now? Compute the answer tothe nearest dollar.
!116. FINANCE A person wishes to have $15,000 cash for a newcar 5 years from now. How much should be placed in an accountnow if the account pays 9.75% compounded weekly? Computethe answer to the nearest dollar.
117. MONEY GROWTH If you invest $5,250 in an account pay-ing 11.38% compounded continuously, how much money willbe in the account at the end of(A) 6.25 years? (B) 17 years?
118. MONEY GROWTH If you invest $7,500 in an accountpaying 8.35% compounded continuously, how much money willbe in the account at the end of(A) 5.5 years? (B) 12 years?
!119. FINANCE If $3,000 is deposited into an account earn-ing 8% compounded daily and, at the same time, $5,000 isdeposited into an account earning 5% compounded daily,will the first account be worth more than the second?If so, when?
!120. FINANCE If $4,000 is deposited into an account earning9% compounded weekly and, at the same time, $6,000 isdeposited into an account earning 7% compounded weekly,
will the first account be worth more than the second? Ifso, when?
!121. FINANCE Will an investment of $10,000 at 8.9% com-pounded daily ever be worth more at the end of any quarter thanan investment of $10,000 at 9% compounded quarterly?Explain.
!122. FINANCE A sum of $5,000 is invested at 13% com-pounded semiannually. Suppose that a second investment of$5,000 is made at interest rate r compounded daily. Both in-vestments are held for 1 year. For which values of r, to thenearest tenth of a percent, is the second investment better thanthe first? Discuss.
!123. PRESENT VALUE A promissory note will pay $30,000 atmaturity 10 years from now. How much should you pay for thenote now if the note gains value at a rate of 9% compoundedcontinuously?
!124. PRESENT VALUE A promissory note will pay $50,000 atmaturity years from now. How much should you pay for thenote now if the note gains value at a rate of 10% compoundedcontinuously?
125. MONEY GROWTH Barron’s, a national business and finan-cial weekly, published the following “Top Savings DepositYields” for -year certificate of deposit accounts:
Gill Savings 8.30% (CC)Richardson Savings and Loan 8.40% (CQ)USA Savings 8.25% (CD)
where CC represents compounded continuously, CQ com-pounded quarterly, and CD compounded daily. Compute thevalue of $1,000 invested in each account at the end of years.
126. MONEY GROWTH Refer to Problem 125. In another issueof Barron’s, 1-year certificate of deposit accounts included:
Alamo Savings 8.25% (CQ)Lamar Savings 8.05% (CC)
Compute the value of $10,000 invested in each account at theend of 1 year.
127. FINANCE Suppose $4,000 is invested at 11% compoundedweekly. How much money will be in the account in(A) year? (B) 10 years?
Compute answers to the nearest cent.
128. FINANCE Suppose $2,500 is invested at 7% compoundedquarterly. How much money will be in the account in(A) year? (B) 15 years?
Compute answers to the nearest cent.
34
12
212
212
512
S E C T I O N 5–1 Exponential Functions 469
CA
*Round monetary amounts to the nearest cent unless specifiedotherwise. In all problems involving interest that is compoundeddaily, assume a 365-day year.
bar67388_ch05_452-469 11/30/06 21:13 Page 469
111. Investigate the behavior of the functions f1(x) ! x!e x,f2(x) ! x2!ex, and f3(x) ! x3!ex as x S " and as x S #",and find any horizontal asymptotes. Generalize tofunctions of the form fn(x) ! xn!ex, where n is any positiveinteger.
112. Investigate the behavior of the functions g1(x) ! xe x,g2(x) ! x2ex, and g3(x) ! x3ex as x S " and as x S #",and find any horizontal asymptotes. Generalize to func-tions of the form gn(x) ! xnex, where n is any positiveinteger.
113. Explain why the graph of an exponential function cannotbe the graph of a polynomial function.
114. Explain why the graph of an exponential function cannotbe the graph of a rational function.
APPLICATIONS*!115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 forthe child’s education 17 years from now? Compute the answer tothe nearest dollar.
!116. FINANCE A person wishes to have $15,000 cash for a newcar 5 years from now. How much should be placed in an accountnow if the account pays 9.75% compounded weekly? Computethe answer to the nearest dollar.
117. MONEY GROWTH If you invest $5,250 in an account pay-ing 11.38% compounded continuously, how much money willbe in the account at the end of(A) 6.25 years? (B) 17 years?
118. MONEY GROWTH If you invest $7,500 in an accountpaying 8.35% compounded continuously, how much money willbe in the account at the end of(A) 5.5 years? (B) 12 years?
!119. FINANCE If $3,000 is deposited into an account earn-ing 8% compounded daily and, at the same time, $5,000 isdeposited into an account earning 5% compounded daily,will the first account be worth more than the second?If so, when?
!120. FINANCE If $4,000 is deposited into an account earning9% compounded weekly and, at the same time, $6,000 isdeposited into an account earning 7% compounded weekly,
will the first account be worth more than the second? Ifso, when?
!121. FINANCE Will an investment of $10,000 at 8.9% com-pounded daily ever be worth more at the end of any quarter thanan investment of $10,000 at 9% compounded quarterly?Explain.
!122. FINANCE A sum of $5,000 is invested at 13% com-pounded semiannually. Suppose that a second investment of$5,000 is made at interest rate r compounded daily. Both in-vestments are held for 1 year. For which values of r, to thenearest tenth of a percent, is the second investment better thanthe first? Discuss.
!123. PRESENT VALUE A promissory note will pay $30,000 atmaturity 10 years from now. How much should you pay for thenote now if the note gains value at a rate of 9% compoundedcontinuously?
!124. PRESENT VALUE A promissory note will pay $50,000 atmaturity years from now. How much should you pay for thenote now if the note gains value at a rate of 10% compoundedcontinuously?
125. MONEY GROWTH Barron’s, a national business and finan-cial weekly, published the following “Top Savings DepositYields” for -year certificate of deposit accounts:
Gill Savings 8.30% (CC)Richardson Savings and Loan 8.40% (CQ)USA Savings 8.25% (CD)
where CC represents compounded continuously, CQ com-pounded quarterly, and CD compounded daily. Compute thevalue of $1,000 invested in each account at the end of years.
126. MONEY GROWTH Refer to Problem 125. In another issueof Barron’s, 1-year certificate of deposit accounts included:
Alamo Savings 8.25% (CQ)Lamar Savings 8.05% (CC)
Compute the value of $10,000 invested in each account at theend of 1 year.
127. FINANCE Suppose $4,000 is invested at 11% compoundedweekly. How much money will be in the account in(A) year? (B) 10 years?
Compute answers to the nearest cent.
128. FINANCE Suppose $2,500 is invested at 7% compoundedquarterly. How much money will be in the account in(A) year? (B) 15 years?
Compute answers to the nearest cent.
34
12
212
212
512
S E C T I O N 5–1 Exponential Functions 469
CA
*Round monetary amounts to the nearest cent unless specifiedotherwise. In all problems involving interest that is compoundeddaily, assume a 365-day year.
bar67388_ch05_452-469 11/30/06 21:13 Page 469
111. Investigate the behavior of the functions f1(x) ! x!e x,f2(x) ! x2!ex, and f3(x) ! x3!ex as x S " and as x S #",and find any horizontal asymptotes. Generalize tofunctions of the form fn(x) ! xn!ex, where n is any positiveinteger.
112. Investigate the behavior of the functions g1(x) ! xe x,g2(x) ! x2ex, and g3(x) ! x3ex as x S " and as x S #",and find any horizontal asymptotes. Generalize to func-tions of the form gn(x) ! xnex, where n is any positiveinteger.
113. Explain why the graph of an exponential function cannotbe the graph of a polynomial function.
114. Explain why the graph of an exponential function cannotbe the graph of a rational function.
APPLICATIONS*!115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 forthe child’s education 17 years from now? Compute the answer tothe nearest dollar.
!116. FINANCE A person wishes to have $15,000 cash for a newcar 5 years from now. How much should be placed in an accountnow if the account pays 9.75% compounded weekly? Computethe answer to the nearest dollar.
117. MONEY GROWTH If you invest $5,250 in an account pay-ing 11.38% compounded continuously, how much money willbe in the account at the end of(A) 6.25 years? (B) 17 years?
118. MONEY GROWTH If you invest $7,500 in an accountpaying 8.35% compounded continuously, how much money willbe in the account at the end of(A) 5.5 years? (B) 12 years?
!119. FINANCE If $3,000 is deposited into an account earn-ing 8% compounded daily and, at the same time, $5,000 isdeposited into an account earning 5% compounded daily,will the first account be worth more than the second?If so, when?
!120. FINANCE If $4,000 is deposited into an account earning9% compounded weekly and, at the same time, $6,000 isdeposited into an account earning 7% compounded weekly,
will the first account be worth more than the second? Ifso, when?
!121. FINANCE Will an investment of $10,000 at 8.9% com-pounded daily ever be worth more at the end of any quarter thanan investment of $10,000 at 9% compounded quarterly?Explain.
!122. FINANCE A sum of $5,000 is invested at 13% com-pounded semiannually. Suppose that a second investment of$5,000 is made at interest rate r compounded daily. Both in-vestments are held for 1 year. For which values of r, to thenearest tenth of a percent, is the second investment better thanthe first? Discuss.
!123. PRESENT VALUE A promissory note will pay $30,000 atmaturity 10 years from now. How much should you pay for thenote now if the note gains value at a rate of 9% compoundedcontinuously?
!124. PRESENT VALUE A promissory note will pay $50,000 atmaturity years from now. How much should you pay for thenote now if the note gains value at a rate of 10% compoundedcontinuously?
125. MONEY GROWTH Barron’s, a national business and finan-cial weekly, published the following “Top Savings DepositYields” for -year certificate of deposit accounts:
Gill Savings 8.30% (CC)Richardson Savings and Loan 8.40% (CQ)USA Savings 8.25% (CD)
where CC represents compounded continuously, CQ com-pounded quarterly, and CD compounded daily. Compute thevalue of $1,000 invested in each account at the end of years.
126. MONEY GROWTH Refer to Problem 125. In another issueof Barron’s, 1-year certificate of deposit accounts included:
Alamo Savings 8.25% (CQ)Lamar Savings 8.05% (CC)
Compute the value of $10,000 invested in each account at theend of 1 year.
127. FINANCE Suppose $4,000 is invested at 11% compoundedweekly. How much money will be in the account in(A) year? (B) 10 years?
Compute answers to the nearest cent.
128. FINANCE Suppose $2,500 is invested at 7% compoundedquarterly. How much money will be in the account in(A) year? (B) 15 years?
Compute answers to the nearest cent.
34
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*Round monetary amounts to the nearest cent unless specifiedotherwise. In all problems involving interest that is compoundeddaily, assume a 365-day year.
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111. Investigate the behavior of the functions f1(x) ! x!e x,f2(x) ! x2!ex, and f3(x) ! x3!ex as x S " and as x S #",and find any horizontal asymptotes. Generalize tofunctions of the form fn(x) ! xn!ex, where n is any positiveinteger.
112. Investigate the behavior of the functions g1(x) ! xe x,g2(x) ! x2ex, and g3(x) ! x3ex as x S " and as x S #",and find any horizontal asymptotes. Generalize to func-tions of the form gn(x) ! xnex, where n is any positiveinteger.
113. Explain why the graph of an exponential function cannotbe the graph of a polynomial function.
114. Explain why the graph of an exponential function cannotbe the graph of a rational function.
APPLICATIONS*!115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 forthe child’s education 17 years from now? Compute the answer tothe nearest dollar.
!116. FINANCE A person wishes to have $15,000 cash for a newcar 5 years from now. How much should be placed in an accountnow if the account pays 9.75% compounded weekly? Computethe answer to the nearest dollar.
117. MONEY GROWTH If you invest $5,250 in an account pay-ing 11.38% compounded continuously, how much money willbe in the account at the end of(A) 6.25 years? (B) 17 years?
118. MONEY GROWTH If you invest $7,500 in an accountpaying 8.35% compounded continuously, how much money willbe in the account at the end of(A) 5.5 years? (B) 12 years?
!119. FINANCE If $3,000 is deposited into an account earn-ing 8% compounded daily and, at the same time, $5,000 isdeposited into an account earning 5% compounded daily,will the first account be worth more than the second?If so, when?
!120. FINANCE If $4,000 is deposited into an account earning9% compounded weekly and, at the same time, $6,000 isdeposited into an account earning 7% compounded weekly,
will the first account be worth more than the second? Ifso, when?
!121. FINANCE Will an investment of $10,000 at 8.9% com-pounded daily ever be worth more at the end of any quarter thanan investment of $10,000 at 9% compounded quarterly?Explain.
!122. FINANCE A sum of $5,000 is invested at 13% com-pounded semiannually. Suppose that a second investment of$5,000 is made at interest rate r compounded daily. Both in-vestments are held for 1 year. For which values of r, to thenearest tenth of a percent, is the second investment better thanthe first? Discuss.
!123. PRESENT VALUE A promissory note will pay $30,000 atmaturity 10 years from now. How much should you pay for thenote now if the note gains value at a rate of 9% compoundedcontinuously?
!124. PRESENT VALUE A promissory note will pay $50,000 atmaturity years from now. How much should you pay for thenote now if the note gains value at a rate of 10% compoundedcontinuously?
125. MONEY GROWTH Barron’s, a national business and finan-cial weekly, published the following “Top Savings DepositYields” for -year certificate of deposit accounts:
Gill Savings 8.30% (CC)Richardson Savings and Loan 8.40% (CQ)USA Savings 8.25% (CD)
where CC represents compounded continuously, CQ com-pounded quarterly, and CD compounded daily. Compute thevalue of $1,000 invested in each account at the end of years.
126. MONEY GROWTH Refer to Problem 125. In another issueof Barron’s, 1-year certificate of deposit accounts included:
Alamo Savings 8.25% (CQ)Lamar Savings 8.05% (CC)
Compute the value of $10,000 invested in each account at theend of 1 year.
127. FINANCE Suppose $4,000 is invested at 11% compoundedweekly. How much money will be in the account in(A) year? (B) 10 years?
Compute answers to the nearest cent.
128. FINANCE Suppose $2,500 is invested at 7% compoundedquarterly. How much money will be in the account in(A) year? (B) 15 years?
Compute answers to the nearest cent.
34
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*Round monetary amounts to the nearest cent unless specifiedotherwise. In all problems involving interest that is compoundeddaily, assume a 365-day year.
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111. Investigate the behavior of the functions f1(x) ! x!e x,f2(x) ! x2!ex, and f3(x) ! x3!ex as x S " and as x S #",and find any horizontal asymptotes. Generalize tofunctions of the form fn(x) ! xn!ex, where n is any positiveinteger.
112. Investigate the behavior of the functions g1(x) ! xe x,g2(x) ! x2ex, and g3(x) ! x3ex as x S " and as x S #",and find any horizontal asymptotes. Generalize to func-tions of the form gn(x) ! xnex, where n is any positiveinteger.
113. Explain why the graph of an exponential function cannotbe the graph of a polynomial function.
114. Explain why the graph of an exponential function cannotbe the graph of a rational function.
APPLICATIONS*!115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 forthe child’s education 17 years from now? Compute the answer tothe nearest dollar.
!116. FINANCE A person wishes to have $15,000 cash for a newcar 5 years from now. How much should be placed in an accountnow if the account pays 9.75% compounded weekly? Computethe answer to the nearest dollar.
117. MONEY GROWTH If you invest $5,250 in an account pay-ing 11.38% compounded continuously, how much money willbe in the account at the end of(A) 6.25 years? (B) 17 years?
118. MONEY GROWTH If you invest $7,500 in an accountpaying 8.35% compounded continuously, how much money willbe in the account at the end of(A) 5.5 years? (B) 12 years?
!119. FINANCE If $3,000 is deposited into an account earn-ing 8% compounded daily and, at the same time, $5,000 isdeposited into an account earning 5% compounded daily,will the first account be worth more than the second?If so, when?
!120. FINANCE If $4,000 is deposited into an account earning9% compounded weekly and, at the same time, $6,000 isdeposited into an account earning 7% compounded weekly,
will the first account be worth more than the second? Ifso, when?
!121. FINANCE Will an investment of $10,000 at 8.9% com-pounded daily ever be worth more at the end of any quarter thanan investment of $10,000 at 9% compounded quarterly?Explain.
!122. FINANCE A sum of $5,000 is invested at 13% com-pounded semiannually. Suppose that a second investment of$5,000 is made at interest rate r compounded daily. Both in-vestments are held for 1 year. For which values of r, to thenearest tenth of a percent, is the second investment better thanthe first? Discuss.
!123. PRESENT VALUE A promissory note will pay $30,000 atmaturity 10 years from now. How much should you pay for thenote now if the note gains value at a rate of 9% compoundedcontinuously?
!124. PRESENT VALUE A promissory note will pay $50,000 atmaturity years from now. How much should you pay for thenote now if the note gains value at a rate of 10% compoundedcontinuously?
125. MONEY GROWTH Barron’s, a national business and finan-cial weekly, published the following “Top Savings DepositYields” for -year certificate of deposit accounts:
Gill Savings 8.30% (CC)Richardson Savings and Loan 8.40% (CQ)USA Savings 8.25% (CD)
where CC represents compounded continuously, CQ com-pounded quarterly, and CD compounded daily. Compute thevalue of $1,000 invested in each account at the end of years.
126. MONEY GROWTH Refer to Problem 125. In another issueof Barron’s, 1-year certificate of deposit accounts included:
Alamo Savings 8.25% (CQ)Lamar Savings 8.05% (CC)
Compute the value of $10,000 invested in each account at theend of 1 year.
127. FINANCE Suppose $4,000 is invested at 11% compoundedweekly. How much money will be in the account in(A) year? (B) 10 years?
Compute answers to the nearest cent.
128. FINANCE Suppose $2,500 is invested at 7% compoundedquarterly. How much money will be in the account in(A) year? (B) 15 years?
Compute answers to the nearest cent.
34
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*Round monetary amounts to the nearest cent unless specifiedotherwise. In all problems involving interest that is compoundeddaily, assume a 365-day year.
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111. Investigate the behavior of the functions f1(x) ! x!e x,f2(x) ! x2!ex, and f3(x) ! x3!ex as x S " and as x S #",and find any horizontal asymptotes. Generalize tofunctions of the form fn(x) ! xn!ex, where n is any positiveinteger.
112. Investigate the behavior of the functions g1(x) ! xe x,g2(x) ! x2ex, and g3(x) ! x3ex as x S " and as x S #",and find any horizontal asymptotes. Generalize to func-tions of the form gn(x) ! xnex, where n is any positiveinteger.
113. Explain why the graph of an exponential function cannotbe the graph of a polynomial function.
114. Explain why the graph of an exponential function cannotbe the graph of a rational function.
APPLICATIONS*!115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 forthe child’s education 17 years from now? Compute the answer tothe nearest dollar.
!116. FINANCE A person wishes to have $15,000 cash for a newcar 5 years from now. How much should be placed in an accountnow if the account pays 9.75% compounded weekly? Computethe answer to the nearest dollar.
117. MONEY GROWTH If you invest $5,250 in an account pay-ing 11.38% compounded continuously, how much money willbe in the account at the end of(A) 6.25 years? (B) 17 years?
118. MONEY GROWTH If you invest $7,500 in an accountpaying 8.35% compounded continuously, how much money willbe in the account at the end of(A) 5.5 years? (B) 12 years?
!119. FINANCE If $3,000 is deposited into an account earn-ing 8% compounded daily and, at the same time, $5,000 isdeposited into an account earning 5% compounded daily,will the first account be worth more than the second?If so, when?
!120. FINANCE If $4,000 is deposited into an account earning9% compounded weekly and, at the same time, $6,000 isdeposited into an account earning 7% compounded weekly,
will the first account be worth more than the second? Ifso, when?
!121. FINANCE Will an investment of $10,000 at 8.9% com-pounded daily ever be worth more at the end of any quarter thanan investment of $10,000 at 9% compounded quarterly?Explain.
!122. FINANCE A sum of $5,000 is invested at 13% com-pounded semiannually. Suppose that a second investment of$5,000 is made at interest rate r compounded daily. Both in-vestments are held for 1 year. For which values of r, to thenearest tenth of a percent, is the second investment better thanthe first? Discuss.
!123. PRESENT VALUE A promissory note will pay $30,000 atmaturity 10 years from now. How much should you pay for thenote now if the note gains value at a rate of 9% compoundedcontinuously?
!124. PRESENT VALUE A promissory note will pay $50,000 atmaturity years from now. How much should you pay for thenote now if the note gains value at a rate of 10% compoundedcontinuously?
125. MONEY GROWTH Barron’s, a national business and finan-cial weekly, published the following “Top Savings DepositYields” for -year certificate of deposit accounts:
Gill Savings 8.30% (CC)Richardson Savings and Loan 8.40% (CQ)USA Savings 8.25% (CD)
where CC represents compounded continuously, CQ com-pounded quarterly, and CD compounded daily. Compute thevalue of $1,000 invested in each account at the end of years.
126. MONEY GROWTH Refer to Problem 125. In another issueof Barron’s, 1-year certificate of deposit accounts included:
Alamo Savings 8.25% (CQ)Lamar Savings 8.05% (CC)
Compute the value of $10,000 invested in each account at theend of 1 year.
127. FINANCE Suppose $4,000 is invested at 11% compoundedweekly. How much money will be in the account in(A) year? (B) 10 years?
Compute answers to the nearest cent.
128. FINANCE Suppose $2,500 is invested at 7% compoundedquarterly. How much money will be in the account in(A) year? (B) 15 years?
Compute answers to the nearest cent.
34
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212
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S E C T I O N 5–1 Exponential Functions 469
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*Round monetary amounts to the nearest cent unless specifiedotherwise. In all problems involving interest that is compoundeddaily, assume a 365-day year.
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111. Investigate the behavior of the functions f1(x) ! x!e x,f2(x) ! x2!ex, and f3(x) ! x3!ex as x S " and as x S #",and find any horizontal asymptotes. Generalize tofunctions of the form fn(x) ! xn!ex, where n is any positiveinteger.
112. Investigate the behavior of the functions g1(x) ! xe x,g2(x) ! x2ex, and g3(x) ! x3ex as x S " and as x S #",and find any horizontal asymptotes. Generalize to func-tions of the form gn(x) ! xnex, where n is any positiveinteger.
113. Explain why the graph of an exponential function cannotbe the graph of a polynomial function.
114. Explain why the graph of an exponential function cannotbe the graph of a rational function.
APPLICATIONS*!115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 forthe child’s education 17 years from now? Compute the answer tothe nearest dollar.
!116. FINANCE A person wishes to have $15,000 cash for a newcar 5 years from now. How much should be placed in an accountnow if the account pays 9.75% compounded weekly? Computethe answer to the nearest dollar.
117. MONEY GROWTH If you invest $5,250 in an account pay-ing 11.38% compounded continuously, how much money willbe in the account at the end of(A) 6.25 years? (B) 17 years?
118. MONEY GROWTH If you invest $7,500 in an accountpaying 8.35% compounded continuously, how much money willbe in the account at the end of(A) 5.5 years? (B) 12 years?
!119. FINANCE If $3,000 is deposited into an account earn-ing 8% compounded daily and, at the same time, $5,000 isdeposited into an account earning 5% compounded daily,will the first account be worth more than the second?If so, when?
!120. FINANCE If $4,000 is deposited into an account earning9% compounded weekly and, at the same time, $6,000 isdeposited into an account earning 7% compounded weekly,
will the first account be worth more than the second? Ifso, when?
!121. FINANCE Will an investment of $10,000 at 8.9% com-pounded daily ever be worth more at the end of any quarter thanan investment of $10,000 at 9% compounded quarterly?Explain.
!122. FINANCE A sum of $5,000 is invested at 13% com-pounded semiannually. Suppose that a second investment of$5,000 is made at interest rate r compounded daily. Both in-vestments are held for 1 year. For which values of r, to thenearest tenth of a percent, is the second investment better thanthe first? Discuss.
!123. PRESENT VALUE A promissory note will pay $30,000 atmaturity 10 years from now. How much should you pay for thenote now if the note gains value at a rate of 9% compoundedcontinuously?
!124. PRESENT VALUE A promissory note will pay $50,000 atmaturity years from now. How much should you pay for thenote now if the note gains value at a rate of 10% compoundedcontinuously?
125. MONEY GROWTH Barron’s, a national business and finan-cial weekly, published the following “Top Savings DepositYields” for -year certificate of deposit accounts:
Gill Savings 8.30% (CC)Richardson Savings and Loan 8.40% (CQ)USA Savings 8.25% (CD)
where CC represents compounded continuously, CQ com-pounded quarterly, and CD compounded daily. Compute thevalue of $1,000 invested in each account at the end of years.
126. MONEY GROWTH Refer to Problem 125. In another issueof Barron’s, 1-year certificate of deposit accounts included:
Alamo Savings 8.25% (CQ)Lamar Savings 8.05% (CC)
Compute the value of $10,000 invested in each account at theend of 1 year.
127. FINANCE Suppose $4,000 is invested at 11% compoundedweekly. How much money will be in the account in(A) year? (B) 10 years?
Compute answers to the nearest cent.
128. FINANCE Suppose $2,500 is invested at 7% compoundedquarterly. How much money will be in the account in(A) year? (B) 15 years?
Compute answers to the nearest cent.
34
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212
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S E C T I O N 5–1 Exponential Functions 469
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*Round monetary amounts to the nearest cent unless specifiedotherwise. In all problems involving interest that is compoundeddaily, assume a 365-day year.
bar67388_ch05_452-469 11/30/06 21:13 Page 469
111. Investigate the behavior of the functions f1(x) ! x!e x,f2(x) ! x2!ex, and f3(x) ! x3!ex as x S " and as x S #",and find any horizontal asymptotes. Generalize tofunctions of the form fn(x) ! xn!ex, where n is any positiveinteger.
112. Investigate the behavior of the functions g1(x) ! xe x,g2(x) ! x2ex, and g3(x) ! x3ex as x S " and as x S #",and find any horizontal asymptotes. Generalize to func-tions of the form gn(x) ! xnex, where n is any positiveinteger.
113. Explain why the graph of an exponential function cannotbe the graph of a polynomial function.
114. Explain why the graph of an exponential function cannotbe the graph of a rational function.
APPLICATIONS*!115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 forthe child’s education 17 years from now? Compute the answer tothe nearest dollar.
!116. FINANCE A person wishes to have $15,000 cash for a newcar 5 years from now. How much should be placed in an accountnow if the account pays 9.75% compounded weekly? Computethe answer to the nearest dollar.
117. MONEY GROWTH If you invest $5,250 in an account pay-ing 11.38% compounded continuously, how much money willbe in the account at the end of(A) 6.25 years? (B) 17 years?
118. MONEY GROWTH If you invest $7,500 in an accountpaying 8.35% compounded continuously, how much money willbe in the account at the end of(A) 5.5 years? (B) 12 years?
!119. FINANCE If $3,000 is deposited into an account earn-ing 8% compounded daily and, at the same time, $5,000 isdeposited into an account earning 5% compounded daily,will the first account be worth more than the second?If so, when?
!120. FINANCE If $4,000 is deposited into an account earning9% compounded weekly and, at the same time, $6,000 isdeposited into an account earning 7% compounded weekly,
will the first account be worth more than the second? Ifso, when?
!121. FINANCE Will an investment of $10,000 at 8.9% com-pounded daily ever be worth more at the end of any quarter thanan investment of $10,000 at 9% compounded quarterly?Explain.
!122. FINANCE A sum of $5,000 is invested at 13% com-pounded semiannually. Suppose that a second investment of$5,000 is made at interest rate r compounded daily. Both in-vestments are held for 1 year. For which values of r, to thenearest tenth of a percent, is the second investment better thanthe first? Discuss.
!123. PRESENT VALUE A promissory note will pay $30,000 atmaturity 10 years from now. How much should you pay for thenote now if the note gains value at a rate of 9% compoundedcontinuously?
!124. PRESENT VALUE A promissory note will pay $50,000 atmaturity years from now. How much should you pay for thenote now if the note gains value at a rate of 10% compoundedcontinuously?
125. MONEY GROWTH Barron’s, a national business and finan-cial weekly, published the following “Top Savings DepositYields” for -year certificate of deposit accounts:
Gill Savings 8.30% (CC)Richardson Savings and Loan 8.40% (CQ)USA Savings 8.25% (CD)
where CC represents compounded continuously, CQ com-pounded quarterly, and CD compounded daily. Compute thevalue of $1,000 invested in each account at the end of years.
126. MONEY GROWTH Refer to Problem 125. In another issueof Barron’s, 1-year certificate of deposit accounts included:
Alamo Savings 8.25% (CQ)Lamar Savings 8.05% (CC)
Compute the value of $10,000 invested in each account at theend of 1 year.
127. FINANCE Suppose $4,000 is invested at 11% compoundedweekly. How much money will be in the account in(A) year? (B) 10 years?
Compute answers to the nearest cent.
128. FINANCE Suppose $2,500 is invested at 7% compoundedquarterly. How much money will be in the account in(A) year? (B) 15 years?
Compute answers to the nearest cent.
34
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212
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S E C T I O N 5–1 Exponential Functions 469
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*Round monetary amounts to the nearest cent unless specifiedotherwise. In all problems involving interest that is compoundeddaily, assume a 365-day year.
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111. Investigate the behavior of the functions f1(x) ! x!e x,f2(x) ! x2!ex, and f3(x) ! x3!ex as x S " and as x S #",and find any horizontal asymptotes. Generalize tofunctions of the form fn(x) ! xn!ex, where n is any positiveinteger.
112. Investigate the behavior of the functions g1(x) ! xe x,g2(x) ! x2ex, and g3(x) ! x3ex as x S " and as x S #",and find any horizontal asymptotes. Generalize to func-tions of the form gn(x) ! xnex, where n is any positiveinteger.
113. Explain why the graph of an exponential function cannotbe the graph of a polynomial function.
114. Explain why the graph of an exponential function cannotbe the graph of a rational function.
APPLICATIONS*!115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 forthe child’s education 17 years from now? Compute the answer tothe nearest dollar.
!116. FINANCE A person wishes to have $15,000 cash for a newcar 5 years from now. How much should be placed in an accountnow if the account pays 9.75% compounded weekly? Computethe answer to the nearest dollar.
117. MONEY GROWTH If you invest $5,250 in an account pay-ing 11.38% compounded continuously, how much money willbe in the account at the end of(A) 6.25 years? (B) 17 years?
118. MONEY GROWTH If you invest $7,500 in an accountpaying 8.35% compounded continuously, how much money willbe in the account at the end of(A) 5.5 years? (B) 12 years?
!119. FINANCE If $3,000 is deposited into an account earn-ing 8% compounded daily and, at the same time, $5,000 isdeposited into an account earning 5% compounded daily,will the first account be worth more than the second?If so, when?
!120. FINANCE If $4,000 is deposited into an account earning9% compounded weekly and, at the same time, $6,000 isdeposited into an account earning 7% compounded weekly,
will the first account be worth more than the second? Ifso, when?
!121. FINANCE Will an investment of $10,000 at 8.9% com-pounded daily ever be worth more at the end of any quarter thanan investment of $10,000 at 9% compounded quarterly?Explain.
!122. FINANCE A sum of $5,000 is invested at 13% com-pounded semiannually. Suppose that a second investment of$5,000 is made at interest rate r compounded daily. Both in-vestments are held for 1 year. For which values of r, to thenearest tenth of a percent, is the second investment better thanthe first? Discuss.
!123. PRESENT VALUE A promissory note will pay $30,000 atmaturity 10 years from now. How much should you pay for thenote now if the note gains value at a rate of 9% compoundedcontinuously?
!124. PRESENT VALUE A promissory note will pay $50,000 atmaturity years from now. How much should you pay for thenote now if the note gains value at a rate of 10% compoundedcontinuously?
125. MONEY GROWTH Barron’s, a national business and finan-cial weekly, published the following “Top Savings DepositYields” for -year certificate of deposit accounts:
Gill Savings 8.30% (CC)Richardson Savings and Loan 8.40% (CQ)USA Savings 8.25% (CD)
where CC represents compounded continuously, CQ com-pounded quarterly, and CD compounded daily. Compute thevalue of $1,000 invested in each account at the end of years.
126. MONEY GROWTH Refer to Problem 125. In another issueof Barron’s, 1-year certificate of deposit accounts included:
Alamo Savings 8.25% (CQ)Lamar Savings 8.05% (CC)
Compute the value of $10,000 invested in each account at theend of 1 year.
127. FINANCE Suppose $4,000 is invested at 11% compoundedweekly. How much money will be in the account in(A) year? (B) 10 years?
Compute answers to the nearest cent.
128. FINANCE Suppose $2,500 is invested at 7% compoundedquarterly. How much money will be in the account in(A) year? (B) 15 years?
Compute answers to the nearest cent.
34
12
212
212
512
S E C T I O N 5–1 Exponential Functions 469
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*Round monetary amounts to the nearest cent unless specifiedotherwise. In all problems involving interest that is compoundeddaily, assume a 365-day year.
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111. Investigate the behavior of the functions f1(x) ! x!e x,f2(x) ! x2!ex, and f3(x) ! x3!ex as x S " and as x S #",and find any horizontal asymptotes. Generalize tofunctions of the form fn(x) ! xn!ex, where n is any positiveinteger.
112. Investigate the behavior of the functions g1(x) ! xe x,g2(x) ! x2ex, and g3(x) ! x3ex as x S " and as x S #",and find any horizontal asymptotes. Generalize to func-tions of the form gn(x) ! xnex, where n is any positiveinteger.
113. Explain why the graph of an exponential function cannotbe the graph of a polynomial function.
114. Explain why the graph of an exponential function cannotbe the graph of a rational function.
APPLICATIONS*!115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 forthe child’s education 17 years from now? Compute the answer tothe nearest dollar.
!116. FINANCE A person wishes to have $15,000 cash for a newcar 5 years from now. How much should be placed in an accountnow if the account pays 9.75% compounded weekly? Computethe answer to the nearest dollar.
117. MONEY GROWTH If you invest $5,250 in an account pay-ing 11.38% compounded continuously, how much money willbe in the account at the end of(A) 6.25 years? (B) 17 years?
118. MONEY GROWTH If you invest $7,500 in an accountpaying 8.35% compounded continuously, how much money willbe in the account at the end of(A) 5.5 years? (B) 12 years?
!119. FINANCE If $3,000 is deposited into an account earn-ing 8% compounded daily and, at the same time, $5,000 isdeposited into an account earning 5% compounded daily,will the first account be worth more than the second?If so, when?
!120. FINANCE If $4,000 is deposited into an account earning9% compounded weekly and, at the same time, $6,000 isdeposited into an account earning 7% compounded weekly,
will the first account be worth more than the second? Ifso, when?
!121. FINANCE Will an investment of $10,000 at 8.9% com-pounded daily ever be worth more at the end of any quarter thanan investment of $10,000 at 9% compounded quarterly?Explain.
!122. FINANCE A sum of $5,000 is invested at 13% com-pounded semiannually. Suppose that a second investment of$5,000 is made at interest rate r compounded daily. Both in-vestments are held for 1 year. For which values of r, to thenearest tenth of a percent, is the second investment better thanthe first? Discuss.
!123. PRESENT VALUE A promissory note will pay $30,000 atmaturity 10 years from now. How much should you pay for thenote now if the note gains value at a rate of 9% compoundedcontinuously?
!124. PRESENT VALUE A promissory note will pay $50,000 atmaturity years from now. How much should you pay for thenote now if the note gains value at a rate of 10% compoundedcontinuously?
125. MONEY GROWTH Barron’s, a national business and finan-cial weekly, published the following “Top Savings DepositYields” for -year certificate of deposit accounts:
Gill Savings 8.30% (CC)Richardson Savings and Loan 8.40% (CQ)USA Savings 8.25% (CD)
where CC represents compounded continuously, CQ com-pounded quarterly, and CD compounded daily. Compute thevalue of $1,000 invested in each account at the end of years.
126. MONEY GROWTH Refer to Problem 125. In another issueof Barron’s, 1-year certificate of deposit accounts included:
Alamo Savings 8.25% (CQ)Lamar Savings 8.05% (CC)
Compute the value of $10,000 invested in each account at theend of 1 year.
127. FINANCE Suppose $4,000 is invested at 11% compoundedweekly. How much money will be in the account in(A) year? (B) 10 years?
Compute answers to the nearest cent.
128. FINANCE Suppose $2,500 is invested at 7% compoundedquarterly. How much money will be in the account in(A) year? (B) 15 years?
Compute answers to the nearest cent.
34
12
212
212
512
S E C T I O N 5–1 Exponential Functions 469
CA
*Round monetary amounts to the nearest cent unless specifiedotherwise. In all problems involving interest that is compoundeddaily, assume a 365-day year.
bar67388_ch05_452-469 11/30/06 21:13 Page 469
111. Investigate the behavior of the functions f1(x) ! x!e x,f2(x) ! x2!ex, and f3(x) ! x3!ex as x S " and as x S #",and find any horizontal asymptotes. Generalize tofunctions of the form fn(x) ! xn!ex, where n is any positiveinteger.
112. Investigate the behavior of the functions g1(x) ! xe x,g2(x) ! x2ex, and g3(x) ! x3ex as x S " and as x S #",and find any horizontal asymptotes. Generalize to func-tions of the form gn(x) ! xnex, where n is any positiveinteger.
113. Explain why the graph of an exponential function cannotbe the graph of a polynomial function.
114. Explain why the graph of an exponential function cannotbe the graph of a rational function.
APPLICATIONS*!115. FINANCE A couple just had a new child. How much should
they invest now at 8.25% compounded daily to have $40,000 forthe child’s education 17 years from now? Compute the answer tothe nearest dollar.
!116. FINANCE A person wishes to have $15,000 cash for a newcar 5 years from now. How much should be placed in an accountnow if the account pays 9.75% compounded weekly? Computethe answer to the nearest dollar.
117. MONEY GROWTH If you invest $5,250 in an account pay-ing 11.38% compounded continuously, how much money willbe in the account at the end of(A) 6.25 years? (B) 17 years?
118. MONEY GROWTH If you invest $7,500 in an accountpaying 8.35% compounded continuously, how much money willbe in the account at the end of(A) 5.5 years? (B) 12 years?
!119. FINANCE If $3,000 is deposited into an account earn-ing 8% compounded daily and, at the same time, $5,000 isdeposited into an account earning 5% compounded daily,will the first account be worth more than the second?If so, when?
!120. FINANCE If $4,000 is deposited into an account earning9% compounded weekly and, at the same time, $6,000 isdeposited into an account earning 7% compounded weekly,
will the first account be worth more than the second? Ifso, when?
!121. FINANCE Will an investment of $10,000 at 8.9% com-pounded daily ever be worth more at the end of any quarter thanan investment of $10,000 at 9% compounded quarterly?Explain.
!122. FINANCE A sum of $5,000 is invested at 13% com-pounded semiannually. Suppose that a second investment of$5,000 is made at interest rate r compounded daily. Both in-vestments are held for 1 year. For which values of r, to thenearest tenth of a percent, is the second investment better thanthe first? Discuss.
!123. PRESENT VALUE A promissory note will pay $30,000 atmaturity 10 years from now. How much should you pay for thenote now if the note gains value at a rate of 9% compoundedcontinuously?
!124. PRESENT VALUE A promissory note will pay $50,000 atmaturity years from now. How much should you pay for thenote now if the note gains value at a rate of 10% compoundedcontinuously?
125. MONEY GROWTH Barron’s, a national business and finan-cial weekly, published the following “Top Savings DepositYields” for -year certificate of deposit accounts:
Gill Savings 8.30% (CC)Richardson Savings and Loan 8.40% (CQ)USA Savings 8.25% (CD)
where CC represents compounded continuously, CQ com-pounded quarterly, and CD compounded daily. Compute thevalue of $1,000 invested in each account at the end of years.
126. MONEY GROWTH Refer to Problem 125. In another issueof Barron’s, 1-year certificate of deposit accounts included:
Alamo Savings 8.25% (CQ)Lamar Savings 8.05% (CC)
Compute the value of $10,000 invested in each account at theend of 1 year.
127. FINANCE Suppose $4,000 is invested at 11% compoundedweekly. How much money will be in the account in(A) year? (B) 10 years?
Compute answers to the nearest cent.
128. FINANCE Suppose $2,500 is invested at 7% compoundedquarterly. How much money will be in the account in(A) year? (B) 15 years?
Compute answers to the nearest cent.
34
12
212
212
512
S E C T I O N 5–1 Exponential Functions 469
CA
*Round monetary amounts to the nearest cent unless specifiedotherwise. In all problems involving interest that is compoundeddaily, assume a 365-day year.
bar67388_ch05_452-469 11/30/06 21:13 Page 469
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