A general exponential function has the form
are positive real numbers. The number
is called the exponential base and the number
is called the multiplicative constant.
If the base
, then the function is one of exponential growth and the function is always increasing. If the base
, then the function is one of exponential decay and is therefore always decreasing.
There are two special points to keep in mind to help sketch the graph of an exponential function: At
Here are three other properties of an exponential function:
intercept is always at
• There are no
intercepts. In fact, the exponential function has horizontal asymptote at
• The graph is always above the