Exponential Growth and Decay

1. The population of rabbits in Mapleton County is growing at a rate of 13.5% per year. If there is a current population estimated at about 1500, how many will there be in 10 years?

2. If the value of a laptop computer depreciates at 20% per year, how much will a $900 laptop be worth in 5 years?

3. The population of Maryborough is currently 10500. It has been growing at 7.5%/year. If this rate of growth continues, what will the population be in 25 years?

4. A new Ferrari, fully loaded sells at $300 000, but depreciates at 13%/year. How much will it be worth used after 10 years?

5. The population of a colony of bacteria doubles every 4 hours. The current population is 1000. Determine the population in: a. 1 day b. 18 hours c. 24 hours ago

6. The half-life of caffeine in the bloodstream of an 8 year old child is approximately 2.5 hours. If Joey (8) eats a chocolate bar containing 110mg of caffeine, how much caffeine is left in his bloodstream after: a. 5 hours b. 12 hours c. 1 day

7. When a basketball is correctly inflated it rebounds to approximately 60% of the height from which it is dropped. If a correctly inflated basketball is dropped from a height of 2.2m and continues to bounce each time rebounding at 60% of its height, determine the height after 5 rebounds.

8. In 1995, the population of Calgary was 828 500, and was increasing at the rate of 2.2% per year.

a) Write an equation to represent the population of Calgary, P, as a function of the number of years, y since 1995. b) Determine how many years it will take for the population to double, to the nearest year. c) Write the equation in part a as an exponential function with base 2.

9. The battery in a cell phone loses 2% of its charge each day. Assume the battery is 100% charged. a) Write an equation to represent the percent charge, P, as a function of the number of days, d, since the battery was charged. b) Determine the number of days until the battery is only 50% charged. c) Write the equation in part a as an exponential function with base 1 . 2

10. For every metre below the surface of the water, the intensity of light is reduced by 4.5%.

a) Write an equation to represent the percent , P, of surface light as a function of the depth, d metres. b) Determine the depth, to the nearest metre, at which one-half the light has disappeared. c) Write the equation in part a as an exponential function with base 1 . 2

11.a) Calculate the number of years for an investment of $1000 to double at an interest rate of 7.2% compounded annually. b) Write the equation in part a as an exponential function with base 2.

12. Polonium-210 is a radioactive element with a half-life of 20 weeks. From a sample of 25 g, how much would remain after 14 weeks? Answer accurate to one decimal place.

13. The half-life of sodium-24 is 14.9 hours. Suppose a hospital buys a 40-mg sample of sodium-24.

a) How much of the sample, accurate to one decimal place, will remain after 48 hours? b) How long will it be until only 1 mg remains?

14. The population of a colony of bacteria can double in 25 minutes. After one hour, how many times as great is the population as it is after 25 minutes? Answer accurate to one decimal place.

ANSWERS 1. 5322 2. 294.91 3. 64 033 4. $74527.02 5.a) 64000 b) 22 627 c) 16 6.a) 27.5mg b) 3.95mg c) 0.14mg 7. 17cm y y 8. a) P = 828500( 1.022) b) 32 years c) P = 828500( 2)32 d d 骣1 34 9. a) P = 100( 0.98) b) 34 days c) P = 100琪桫2 d d 骣1 15 10. a) P = 100( 0.955) b) 15 m c) P = 100琪桫2 x 11. a) 10 years b) y = 1000( 2)10 12. 15.4 g 13. a) 4.3 mg 79.3 h 14. 2.6