Name:___________________________________________ Block:________ Date:____________________________________
Exponential Growth and Decay Word Problems
For each equation below, identify the equation as exponential growth or decay, its initial
value, the growth (or decay) factor, and the growth (or decay) rate.
3. 𝑦 = 4.5(4)𝑥
1. 𝑦 = 3.34(1.67)𝑥
2. 𝑦 = 8(. 54)𝑥
4. 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? By what percent did the
population increase by each year?
5. The Boston Red Sox sign a new player for $8,000,000 and his salary goes up by 3% every
year.
a. Initial value:
b. Growth factor:
c. Equation:
d. How much will the player make in 4 years?
6. A super-deadly strain of bacteria is turning people into zombies. The zombie population
doubles each day. Currently, there are 25 zombies. Write an equation to determine how
many zombies there will be in 5 days.
7. Over the last several years there has been an increase in the amount of school age children
carrying cell phones. Current estimates are that there are 1,237,000 students in the US with
cell phones. The trend is likely to continue, with the amount of children with phones
tripling every decade.
a. Write an equation to determine the number of students carrying cellphones in x
decades.
b. How many students will have cell phones by 2045? (Think CAREFULLY about what
your x value will be here!)
8.
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?
9. You deposit $1600 in a bank account. Find the balance after 3 years if account pays 4%
annual interest.
10. You buy a new computer for $2400. The computer decreases by 50% annually. When will
the computer have a value of $600?
11. You drink a beverage with 120 mg of caffeine. Each hour, the caffeine in your system
decreases by about 12%. How much caffeine will be in your system in 4 hours?
12. The world population in 2005 was approximately 6.47 billion. The annual rate of increase
was about 1.3%.
a. Find the growth factor for the world population.
b. Suppose the rate of increase continues to be 1.3%. Let 𝑥 be the number of years past
the year 2005. Write a function to model the world population.
c. Find the world population in 2015 and 2025
13. A new truck that sells for $29,000 depreciates 12% each year. Write a function that models
the value of the truck. Find the value of the truck after 7yrs.
For #14 and #15, answer the questions and create a graph for each (a table may be helpful).
14. You purchase a stereo system for $830. The value of the stereo system decreases 13% each
year.
a. Write an exponential decay equation for the value of the stereo system in terms of
the number of years since the purchase.
b. Make a table and graph the function:
𝑥
𝑦
0
1
2
5
10
c. Use your graph to estimate when the stereo will be worth $270. Confirm using your
equation.
15. In 2000, the tuition at a private college was $30,000. During the next 10 years, tuition
increased by about 7.2% each year.
a. Write an equation giving the cost C of tuition at the college t years after 1990.
b. Make a table and graph the function:
𝑥
𝑦
0
1
5
10
25
c. Use your graph to estimate when the
cost will reach $60,000