Algebra 1
Name: ________________________
Date: _________________________
Class#: _______________________
7.7 Exponential Growth and Decay
Identify each problem as exponential growth or decay. Identify the initial value, the growth/decay
rate, the time, and the growth factor. Write the simplified formula with the given values in the word
problem. Then use your formula to evaluate and answer the question.
1. An initial population of 1000 starfish doubles each year for 4 years. Write an equation that
describes this situation. Determine the starfish population after 4 years.
a. Identify the given variables:
a:
r:
t:
b. Write the simplified formula for the given situation:
Growth/Decay Formula:
Simplified:
Growth/Decay Factor:
c. Evaluate for the time given in the problem.
2. Your friend bought a car for $24,000. The car depreciates at the rate of 10% per year. Write an
exponential decay model to represent the car’s value. Determine the value of his car in 3 years.
a. Identify the given variables:
a:
r:
t:
b. Write the simplified formula for the given situation:
Growth/Decay Formula:
Simplified:
Growth/Decay Factor:
c. Evaluate for the time given in the problem.
3. There are a total of 128 teams at the start of a citywide 3-on-3 basketball tournament. Half of the
teams are eliminated after each round. Identify the initial amount, the decay rate, and the decay
factor. Write a function for the number of teams left after x rounds. Use this function to
determine when there 4 teams left in the tournament.
a. Identify the given variables:
a:
r:
t:
b. Write the simplified formula for the given situation:
Growth/Decay Formula:
Simplified:
Growth/Decay Factor:
c. Evaluate for the time given in the problem.
4. One computer industry expert reported that there were about 600 million computers in use
worldwide in 2001 and that the number was increasing at an annual rate of about 10%. Write a
function that models the number of computers in use over time, where x is the number of years
since 2001 and f(x) is the number of computers in millions. Predict the number of computers that
will be in use worldwide in 2014.
a. Identify the given variables:
a:
r:
t:
b. Write the simplified formula for the given situation:
Growth/Decay Formula:
Simplified:
Growth/Decay Factor:
c. Evaluate for the time given in the problem.
5.
An annual benefit concert attendance of 10,000 increases by 5% each year. Write an equation
that describes this situation. Predict the attendance at this concert after 7 years.
a. Identify the given variables:
a:
r:
t:
b. Write the simplified formula for the given situation:
Growth/Decay Formula:
Simplified:
Growth/Decay Factor:
c. Evaluate for the time given in the problem.
6. Membership in an after-school athletic club declined at a rate of 5% per year for the period 20002005. There were 54 members in 2000. Identify the initial amount, whether growth or decay, the
rate, and the factor. Write a function that describes this situation. Use this model to determine in
what year the club had 45 members.
a. Identify the given variables:
a:
r:
t:
b. Write the simplified formula for the given situation:
Growth/Decay Formula:
Simplified:
Growth/Decay Factor:
c. Evaluate for the time given in the problem.
7. A recent college graduate accepts a job at a law firm. The job has a salary of $32,000 per year.
The law firm guarantees an annual pay increase of 3% of the employee’s salary. Write a
function that models the employee’s salary over time. Assume that the employee receives only
the guaranteed pay increase. Use the function to find the employee’s salary after 5 years.
a. Identify the given variables:
a:
r:
t:
b. Write the simplified formula for the given situation:
Growth/Decay Formula:
Simplified:
Growth/Decay Factor:
c. Evaluate for the time given in the problem.
8.
Scientists studied the population of a species of bat in some caves in Missouri from 1983 to
2003. In 1983, there were 141,200 bats living in the caves. That number decreased by about 11%
annually until 2003. Identify the initial amount, the decay factor, and the decay rate. Write a
function that models the number of bats since 1983. Then find the number of bats in 2003.
a. Identify the given variables:
a:
r:
t:
b. Write the simplified formula for the given situation:
Growth/Decay Formula:
Simplified:
Growth/Decay Factor:
c. Evaluate for the time given in the problem.
9.