Name ______Date ______Block ______
Exponential Growth & Decay Practice Problems
Exponential Growth Formula: A = P(1 + r)t Where P = original amount, r = rate in decimals, t = time in years
Exp. Growth (when interest is compounded): A = P(1 + r/n)nt n = number of times compounded per year
Exponential Decay Formula: A = P(1 – r)t
When you are trying to find out the value of something “so many years ago”, use a negative exponent!
1. The population of a city grows at a yearly rate of 1.5%. the city has a current population of 500,000. Predict the population of the city two years from now.
Equation: ______Predicted population: ______
2. A city has a current population of 700,000 people and a yearly growth rate of 6.5%. Predict the population after:
2 years: ______4 years: ______10 years ago: ______
Given the following data, estimate the population of each city:
3. current population: 1,000,000; growth rate 4.5%, after 5 years: ______
4. current population: 350,000; growth rate: 7%, after 3 years: ______
5. current population: 8,200,000; growth rate: 11.4%, after 4 years: ______
6. The current population in 2011 of a city is 120,000. It is estimated that the population will grow 1.5% annually. What will the city’s population be in 2025?
______
7. An investment has been losing money at a rate of 3% per year and now has a value of $6500. What was the value of the investment 5 years ago?
______
An investment is growing at a rate of 5.5% per year and now has a value of $6300. Find the value of the investment …
8. in 5 years: ______9. 5 years ago: ______
10. in 10 years: ______11. 10 years ago: ______
12. A baseball card that originally cost $24 has been decreasing in value at an annual rate of 6% for the last 5 years. What is the present value?
______
13. A large city has a population of 500,000 and has been increasing in size at an annual rate of 2% for 6 years. What was its population 6 years ago?
______
14. One share of stock that originally sold for $54 has increased in value at an annual rate of 4% for the last 7 years. What is its present value?
______
15. The international Telecommunications Union estimated 130,000,000 telephone subscribers in the United States in 1991. The number of telephone subscribers is estimated to increase each year by 5%. Estimate the number of subscribers in 2011.
______
16. The “Mendelssohn” Stradivarius violin was estimated to be worth approximately $1,700,000 in 1990. The violin is expected to increase in value by approximately 7.5% each year. Estimate the value of the violin in the year 2025.
______
17. The value of a condominium has increased in value 3% per year for 5 years. If the condominium is worth $128,500 now, what was its value 5 years ago?
______
18. Using the same condominium from question 17, what will the value be worth 10 years from now?
______
19. Mr. Jones bought a new BMW for $48,952 in 2008. The value of this car depreciates at a rate of 4% per year. What will the value of his car be in the year 2016?
______
20. – 21. Does the table below show exponential behavior?
X / -5 / 0 / 5 / 10Y / 100 / 200 / 400 / 800
X / -1 / 0 / 1 / 2
Y / 2 / 4 / 6 / 8