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         2.2   Checkpoint Exponential Functions:  Decay

1. Write an exponential function with an initial value of 50,000 and a decay rate of 3%.

2. Write an exponential function with an initial value of 1,000 and a decay rate of 5%.

3. How many people would live in a town after 5 years if 30,000 people lived there originally and 10% skipped town every year?

4. How many people would live in a town after 8 years if 10,000 people lived there originally and 1% skipped town every year?

5. Explain why in the formula   the constant C  represents the initial amount of your quantity, given that the variable t  represents time.

     6.  The amount (in milligrams) of a drug in the body t hours after taking a pill is given by

         .

a)    What is the initial dose given?

b)   What percent of the drug leaves the body each hour?

c)    What is the amount of the drug left after 10 hours?

d)   After how many hours will there be less than 1 milligram left in the body?*

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*NOTE: Problem #6 is from Connally, Hughes-Hallett, Gleason et al. Functions Modeling Change. A Preparation for Calculus.  New York:  John Wiley & Sons, 2000, p. 111.