Name: Algebra 2 Date: Review for Test on Exponents, Logs, and Exponential Functions You will be responsible for the following topics: Exponent properties Negative exponents Fraction exponents Simplifying expressions using exponent properties (including fraction and negative exponents) Simplifying expressions with logarithms Solving equations with exponents and logarithms Exponential modeling (word problems): o Given a % rate of increase or decrease, find and use an exponential function o Given an input-output pair and a multiplier, find the starting value o Given an exponential function, find the % rate of increase or decrease o Given a starting amount and another point, find the exponential function and the % rate of increase or decrease o Given a starting value, multiplier, and output, find the exponent Review Problems: Part 1-Simplify the following. Do not use your calculator for Part 1. 1. 2. 3. 4.
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Name: Algebra 2Date:
Review for Test on Exponents, Logs, and Exponential Functions
You will be responsible for the following topics:
Exponent properties Negative exponents Fraction exponents Simplifying expressions using exponent properties (including fraction and negative exponents) Simplifying expressions with logarithms Solving equations with exponents and logarithms Exponential modeling (word problems):
o Given a % rate of increase or decrease, find and use an exponential functiono Given an input-output pair and a multiplier, find the starting valueo Given an exponential function, find the % rate of increase or decreaseo Given a starting amount and another point, find the exponential function and the % rate of
increase or decreaseo Given a starting value, multiplier, and output, find the exponent
Review Problems:Part 1-Simplify the following. Do not use your calculator for Part 1.
1.
2.
3.
4.
5.
6.
7. 51 + 50 + 5 –1
8.
9.
10. 2 –2 + 4 –2
11. (2 + 4) –2
Name: Algebra 2Date:
12.
13.
14.
15.
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20.
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25.
26.
Name: Algebra 2Date:
27.
28.
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31.
32.
33.
34.
35.
36.
Name: Algebra 2Date:
37.
38.
39.
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44.
45.
Part 2: For Part 2 you should use your calculator.
Name: Algebra 2Date:1. Marta has a savings account that pays 1.5% interest annually. She has not made any deposits or withdrawals for many years. Suppose that her current balance is $4,516.32. How much money was in her account 5 years ago? Show how you get your answer.
2. Of all the users of the web service Twitter, Lady Gaga (@ladygaga) has the most followers. At the start of year 2010, she had 3,200,000 followers. Her number of followers has been steadily increasing by 8% each month.
a. Let f(x) stand for how many followers @ladygaga has, x months after the start of year 2010. Write a function formula for f(x).
b. How many followers did @ladygaga have at the start of 2011?
c. Solve graphically using the 2nd trace-intersect function on your calculator or by algebra using logarithms. Round your answer to two decimal places. When did the number of followers of @ladygaga surpass 5,000,000 ?
d. Solve graphically using the 2nd trace-intersect function on your calculator or by algebra using logarithms. Round your answer to two decimal places Solve the equation f(x) = 10,000,000. Explain the meaning of the answer as it relates to @ladygaga on Twitter.
3. Giovanna has a bank certificate that pays 2.25% interest monthly. (Increases by 2.25% each month) She does not make any additional deposits or withdrawals. Her current balance is $6,543.21.
Name: Algebra 2Date:
a. How much was this certificate worth 2 years ago?
b. How much will the certificate be worth, 10 months from now?
4. Mrs. Chang owns a painting whose value has been growing exponentially. In the 6 years she’s owned the painting, its value has grown from $20,000 to $30,000.
By about what percent did the painting’s value grow each year?
5. Mrs. Jones owns a painting whose value has been decreasing exponentially. In the 12 years she’s owned the painting, its value has decreases from $40,000 to $10,000.
By about what percent did the painting’s value decrease each year?
6. Mr. Patrick owns a classic car whose value has been increasing by 3.5% each year. The car is worth $5000. He wants to sell the car when it is worth $10,000. How many years must he wait?
Name: Algebra 2Date:Answers:
Part 1:
1. 2. 3. 4.
5. 6. 7. 8.
9. 10. 11. 12.
13. 14. 15. 16.
17. 18. 19. 20.
21. 22. 1 23. 24.
25. 26. 15 27. -4 28. 0
29. 11/2 30. -6 31. 9 32. -8
33. 6 34. -1/2 35. 1/2 36. x = 16
37. x = 6 38. x = 16 39. x = -1 40. x = 5
41. x = -3 42. x = -11 43. x = 2 44. x = 1
45. x = 8
Name: Algebra 2Date:Part 2:
1. 4516.32 · (1.015)–5 = 4192.32, so the balance 5 years ago was $4,192.32.
2. a.
b. f(12) ≈ 8,058,144 so a little over 8 million followers
c. The graphs of Y1=3200000 · 1.08x and Y2= 5000000 intersect at x ≈ 5.8, so it took about 5.8 months from the start of the year, meaning that it happened in late June 2010.
d. Same method as part c, x ≈ 14.8, so it took about 14.8 months from the start of 2010, so around late-March 2011, for Lady Gaga to have 10,000,000 followers.
3. a.
b.
4.
So, the value of the painting grew by 6.991% per year or about 7% per year.
5.
So the painting’s value decreased by about 10.9% per year
6. Y1=
Y2=10,000
x=20.15 years
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