The Exponential and Logarithmic Functions

Abstract

An important class of nonlinear functions that is of particular interest in economics comprises the exponential and logarithmic functions. These functions are useful for investigating problems associated with economic growth and decay and mathematical problems in finance such as the compounding of interest on an investment or the depreciation of an asset. For example, if a person invests £3,000 in an investment bond for which there is a guaranteed annual rate of interest of 5% for two years, the evaluation of an exponential function will provide the return at the end of that period. If a credit card company charges interest on an outstanding balance, the evaluation of an exponential function will provide information on the AER (annual equivalent rate). We begin this chapter by sketching the graphs of some exponential functions and highlighting some of their important properties. Exponential functions are functions in which a constant base a is raised to a variable exponent x. The general form of an exponential function is given by y = ax, where a > 0 and a ≠ 1. (5.1) The parameter a is known as the base of the exponential function. The independent variable x occurs as the exponent of the base.