Section 7.2 Worksheet:

Assigned problems: Exercises pp. 425-428, #2, 5, 16, 24, 26, 56, 57, 59 (you might try finding a reasonable model yourself, then cheat and compare yours with that in the Appendix), 61, 70, 76 (due Wednesday).

1. Once again, we encounter a result (a definition, in this case: #1, pa. 417) which requires that we distinguish between rational and irrational numbers. What's the issue?

2. There are four important properties of exponential functions listed on p. 418: what are they?

3. The most phenomenal property of the exponential function with base e is #9, p. 422. What makes it so special?

4. What are the important graphical properties of an exponential function?

Notes:

1. The exponential function is crucial for many areas of study, from business (where the stock market and your bank account grow exponentially), to biology (populations grow exponentially at times of their life cycles), to all other areas of science.

2. The most important base of an exponential function is . We'll see that one can represent any exponential function, no matter what the base, using e. The exponential function with e as its base is called the natural exponential function.