Practice: Growth and Decay

Practice: Growth and Decay and LOGS Name______

1. In 1990, the population of Idaho was 1,006,749. Since then, that number has increased an average of 2.85% per year.

a. Write an equation to represent the population of Idaho since 1990.

b. According to the equation, what was the population of Idaho in 2000?

c. Determine when the population will be 1,500,000 (USE LOGS!).

2. A computer sells for $2100. The computer depreciates at a rate of 20% per year.

a. Write an equation to represent the value of the computer each year.

b. According to the equation, what will the value of the computer be in 3 years?

c. Determine when the computer will be worth $1500 (USE LOGS!).

3. In 1995 the prairie dog population of a nature preserve was 1,500. Since then, the population has been decreasing by 4.5% per year.

a. Write an equation to represent the prairie population since 1995.

b. Estimate the prairie dog population in 2005.

c. Determine when the population will be 2,000. (USE LOGS!)

4. Anna has $4,000 to attend college in 5 years. Her parents plan to invest the money in an account with an interest rate of 9% compounded monthly for the 5 years.

a. Write an equation to represent the amount of money in the account.

b. How much money will Anna have for college?

c. Determine when the account balance will be $6,000. (USE LOGS!)

5. A boat that costs $8550 decreases in value by 12% per year.

a. How much will the boat be worth after 3 years?

b. Determine when the boat will be worth half its original value. (USE LOGS!)

6. I bought a car for $25,000, but its value is depreciating at a rate of 10% per year.

a. How much will my car be worth after 8 years?

b. Determine when the car will be worth $15,000. (USE LOGS!)

7. A certain species of animal is endangered and its numbers are decreasing 11% annually. There are currently 440 animals in the population.

a. Which is an exponential function representing the population and the estimated number of animals in 5 years?

b. Determine when the population will be cut in half. (USE LOGS!)

8. Suppose you have an initial population of 10 million people and it grows 2% each year. Write an equation to model the population growth.

a. Predict the size of the population after 3 years.

b. Determine when the population will double. (USE LOGS!)

9. A certain species of animal is endangered and its numbers are decreasing 12% annually. There are currently 230 animals in the population.

a.  Which is an exponential function representing the population and the estimated number of animals in 5 years?

b.  Determine when the population will be a fourth of the original population. (USE LOGS!)

10. The Mendoza family just bought a house for $180,000. If the value of the house increases at a rate of 3% per year, about how much will it be worth in 10 years?

A. $250,000

B. $242,000

C. $258,000

D. $234,000

11. A company's projected worth (in millions of dollars) is modeled by the equation y = 236(1.07)x. The variable x represents the number of years since 1997. What is the projected annual percent of growth, and what should the company be worth in 2007?

A. 7%; $433.88 million

B. 7%; $464.25 million

C. 17%; $252.52 million

D. 17%; $496.75 million