The exponential function is $y= e^x$. The value $ e$ is a constant ($\approx 2.71828\dots$) and is the base rate of growth shared by all continually growing processes, such as the growth of the human population. Every growth rate can be considered a scaled version of $ e$ (the unit rate of growth).

The graph of $ e^x$ is shown below (in red). We get the graph of $ e^{-x}$ by reflecting it along the $y$ axis (shown in blue).

Logarithm Function

Definition

The logarithm function is $y=\log_ax$. The natural logarithm function is $y=\log_{ e}x$, more commonly denoted $\ln x$. See Logarithms for more information about logarithms