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.)