Name:____________________________________________________ Date: ________
Exponential Growth and Decay
State whether the formula models growth or decay.
1. y  3(.4)
9
5. y   
2
x
x
2. y  .5(9)
x
1
6. y  (3) x
2
3. y  5(1.25)
7. y  .25(3.8)
x
x
1
4. y  5 
 3
x
2
8. y  4 
5
x
Use the formula for growth and decay to solve the following problems.
9. What is the formula for exponential growth?
10. What is the formula for exponential decay?
11. E. coli bacteria double in population every thirty minutes. If the initial population
is 85, what’s the population of bacteria after two hours? After four hours?
12. Strapped for cash, you decide to borrow money from a local crime lord. This
turns out to be yet another instance of poor judgment on your part. At 22%
interest per year, how much will you owe on a loan of $5,000 after one year?
What about after three years?
13. A serial killer is stalking the residents of Gloomy Falls, Mass., population 937.
Every year the population diminishes by 4.5%. How many residents are left after
the killer’s three-year rampage? HOW WILL YOU STOP HIM?
14. You bought a Boston Whaler in 2004 for $12,500. The boat’s value depreciates
by 7% a year. How much is the boat worth now? What will it be worth in 2020?
15. In 1985, there were 285 cell phone subscribers in the small town of Centerville. The
number of subscribers increased by 75% per year after 1985. How many cell phone
subscribers were in Centerville in 1994?
16. Each year the local country club sponsors a tennis tournament. Play starts with 128
participants. During each round, half of the players are eliminated. How many players
remain after 5 rounds?
17. The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)t where t is
the number of years since 1990. What was the population in 1990? What is the
population now?
18. You have inherited land that was purchased for $30,000 in 1960. The value of the
land increased by approximately 5% per year. What is the approximate value of the
land in the year 2011?
19. During normal breathing, about 12% of the air in the lungs is replaced after one
breath. Write an exponential decay model for the amount of the original air left in the
lungs if the initial amount of air in the lungs is 500 mL. How much of the original air
is present after 240 breaths?
20. Carbon-14 has a half life of 5,700 years. Scientists use this fact to determine the age
of things made of organic material. Suppose the average page of a book containing
0.5 mg of carbon-14 is put into a time capsule. How much carbon-14 will each page
contain in 11,400 years? How much in 17,100 years?