Objectives: In this tutorial, we look at the definition of the exponential function and some of its properties. We investigate what it means to raise a number to an irrational power. The graphs of various exponential functions are compared; in addition, a comparison with the graphs of polynomial functions is made. The number e is introduced. There is an exploration which looks at the approximation of the natural exponential function by polynomials. After working through these materials, the student should be able