# Exponential Function

- Author:
- Dr. Doug Davis, 3D

## Description

The exponential function , , varies its behavior if the base, , is negative or positive. If the base is negative, it is real for only some values of . If is a rational number with an odd denominator, the denominator portion gives a real negative number results. If the numerator is even the final result is positive and if the numerator is odd, the final result is negative.
In this applet , if the base is negative, rational numbers with 5, 7, and 9 in the denominator are shown. If the base is positive the smooth curve is shown.