7-7 Exponential Growth and Decay - KTL MATH CLASSES · 2020-03-17 · 221 Lesson 7-7 Check off the vocabulary words that you understand. exponential growth compound interest exponential
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Got It? Suppose that in 1985, there were 285 cell phone subscribers in a small town. The number of subscribers increased by 75% each year after 1985. How many cell phone subscribers were in the small town in 1994? Write an expression to represent the equivalent monthly cell phone subscription increase.
8. Use the words exponent, growth factor, and initial amount to complete the diagram. Then find the value of the expression to the nearest whole number.
HSM11_A1MC_0707_T91262
9285 ∙ 1.75 value ofthe expression
new population
≈
9. The number of cell phone subscribers in 1994 will be about .
Key Concept Exponential Decay
6. Circle the numbers that could be growth factors.
85% 3 1.05 0.93
7. Circle the numbers that could be decay factors.
85% 3 1.05 0.93
The function y 5 a ? bx, where a . 0 and 0 , b , 1, models exponential decay.
The base b is the decay factor.
Algebra
HSM11_A1MC_0707_T91264
y = a • b x
initial amount (when x = 0)
�e base, which is lessthan 1, is the decay factor.
exponent
The function y 5 a ? bx, where a . 0 and b . 1, models exponential growth.
The base b is the growth factor.
Algebra
HSM11_A1MC_0707_T91261
y = a • b x
initial amount (when x = 0)
�e base, which is greaterthan 1, is the growth factor.
In one year there are months. In x years there are months.
The yearly growth factor of cell phone subscribers is .
1.75 represents the yearly increase of cell phone subscriptions where x is the number of years.
11. Circle the expression that you could use to find the monthly increase in cell phone use in one year.
1.7512x 1.751
12 1.7512x
12. Let m represent the number of months. Write an expression that represents the equivalent monthly cell phone subscription increase.
Compound Interest
Got It? Suppose that when your friend was born, your friend’s parents deposited $2000 in an account paying 4.5% interest compounded monthly. What will the account balance be after 18 yr?
13. Draw a line from each variable in Column A to its value from the problem in Column B.
Column A Column B
P 18
r 0.045
n 2000
t 12
14. Substitute the values into the formula A 5 PQ1 1 rnR
nt to find the account balance.
15. The balance in the account after 18 yr will be $ .
The formula below gives the balance, A, in an account that earns compound interest. The formula is an exponential function with initial amount P and growth
Rate how well you can model exponential growth and decay.
Modeling Exponential Decay
Got It? The kilopascal is a unit of measure for atmospheric pressure. The atmospheric pressure at sea level is about 101 kilopascals. For every 1000-m increase in altitude, the pressure decreases about 11.5%. What is the pressure at an altitude of 5000 m?
16. Between sea level and 5000 m, the atmospheric pressure will decrease
5000 ÷ , or times.
17. Write and simplify an equation to find the atmospheric pressure at 5000 m.
y 101 (1 )
initial amount(of pressure)
decay factor(1 minus the percent decrease written as a decimal)
exponent(number of times the pressure decreases)
18. To the nearest whole unit, the pressure at 5000 m is about kilopascals.
• Do you UNDERSTAND?
Reasoning How can you simplify the compound interest formula when the interest is compounded annually? Explain.
19. When interest is compounded annually, the value of n in Pa1 1rnbnt