Exercises

1. Suppose that b satisfies b > 1. Explain the relationship between the graphs of

and

2. Suppose that f(x) is an exponential function that satisfies . Find the value of b so that

and compute the value of f(2).

3. Suppose that the population of a certain bacteria can be modeled by an exponential function. In a particular experiment, the number of bacteria was 10,000 at t=0. Four hours later, the number of bacteria was 250,000. Suppose a second experiment is performed under the same conditions, but the number of bacteria at t=0 is only 2000. Show, using the equation for exponential growth, that the predicted number of bacteria after four hours in this second experiment is 50,000.
4. Suppose that for a certain drug, the following results were obtained. Immediately after the drug was administered, the concentration was 3.3 mg/ml. Six hours later, the concentration had dropped to 1.55 mg/ml. Determine the value of k for this drug.
5. Suppose that for the drug in the previous exercise, the maximum safe level is and the minimum effective level is . What is the maximum possible time between doses for this drug?

William W. Farr
Fri Jan 31 14:58:36 EST 1997