Exercises

1.

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

f(x) = b^x

and

$$g(x) = \left( \frac{1}{b}\right) ^x$$

2.

Suppose that f(x) is an exponential function that satisfies $f(\sqrt{5}) = 7$. Find the value of b so that

f(x) = b^x

and compute the value of f(3).

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 50,000 at t=0. Four hours later, the number of bacteria was 150,000. Suppose a second experiment is performed under the same conditions, but the number of bacteria at t=0 is only 20,000. Show, using the equation for exponential growth, that the predicted number of bacteria after four hours in this second experiment is 60,000.

4.

Suppose that for a certain drug, the following results were obtained. Immediately after the drug was administered, the concentration was 4.8 mg/ml. Three hours later, the concentration had dropped to 2.23 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 $M=8 \mbox{ mg/ml}$ and the minimum effective level is $m=1.8 \mbox{ mg/ml}$. What is the maximum possible time between doses for this drug?