An exponential function is a function that looks like where a is some positive number. These functions are monotonic (this means that they are always either increasing or decreasing; they never change from one to the other), and have no zeros. The number a is called the base. If 0 < a < 1 then the function decreases in x, and if a > 1 the function increases. One of the most common exponential functions involves the natural exponent, e, which has a bizarre irrational value.
Exponential functions have the following properties.