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Exponential functions

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1. Do exponential functions only model phenomena that grow, or can they also model phenomena that decay? Explain what is different in the form of the function in each case.

2. True or false: The function "f(x) = 3x" grows three times faster than the function "g(x) = x". Explain.

3. What are the asymptotes of the functions "f(x) = 3x" and "g(x) = log52x"?

4. A cell divides into two identical copies every 4 minutes. How many cells will exist after 3 hours?

5. The level of thorium in a sample decreases by a factor of one-half every 4.2 million years. A meteorite is discovered to have only 7.6% of its original thorium remaining. How old is the meteorite?

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This provides several examples of using logarithmic functions to solve word problems

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1. Do exponential functions only model phenomena that grow, or can they also model phenomena that decay? Explain what is different in the form of the function in each case.
An exponential function has the form , where . Whether the function is increasing or decreasing depends on the value of . If , then the function models phenomena that decays; if , ...

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