Exponential

Let $a$ be constant. Exponential functions are of the form $$f(x)=a^x.$$ The most commonly used exponential function is $e^x$, where $e$ is the base of the natural logarithm. It can be characterized as the unique solution to the initial value problem $$\left\{ \begin{array}{ll} y'=y \\ y(0)=1. \end{array} \right.$$