You should KNOW

1. That exponential functions are those of the form

f(x) = a^x where a > 0 (but not 1), that the constant a

is called the __base__ of the exponential function, that

the domain of __any__ exponential function is the whole

line, the range is the set of positive reals.

2. The meaning of, say, 2^3.564 or 2^sqrt(3) in terms of

your previous knowledge of the meaning of 2^x when

x is a an ordinary fraction.

3. What the graphs of exponential functions look like:

that such functions are increasing when a > 1 and

decreasing when a < 1. how the graphs of say, 3^x

and 4^x are related to each other, how the graph of

a^x is related to that of (1/a)^x , that exponential functions

are 1-1 and thus have inverses.

4. The difference between, say, 2^x and x^2 !!

5. That there is a special number, called e, which is

approximately 2.718.... that has especially useful

properties when used as the base of an exponential

function.

6. What compound interest is, what __continuously__

__compounded interest__ is, and how an

exponential function with base e can be used to

give a formula to compute this interest.

You should be ABLE TO

1. Evaluate, by hand in simple cases, and using

your calculator in others, exponential function values.

2. Sketch graphs of exponential functions and those

obtained from them by stretching and translating.

3. Solve simple equations involving exponential

functions.

4. Solve a variety of problems about exponential

growth and decay, including compound interest,

population growth, radioactive decay. (This

will be a continuing thread through the next few

topics.)