ON THE EXPONENTIAL FUNCTION

The natural exponential function is one of the most important functions students should learn in calculus classes. The applications range from mathematics, statistics, natural sciences, and economics. Despite its wide use and importance, instructors often struggle with the proper definition. The purpose of this note is to provide a short, self-contained exposition on the natural ex- ponential function exp(x) starting from an accessible definition to the derivation of all of its properties. We will also discuss other common definitions of the exponential function and show its ap- plication in natural sciences.