4 - EXPONENTIAL AND LOGARITHMIC FUNCTIONS

Abstract

This chapter discusses exponential and logarithmic functions. Exponential functions arise in nature and are useful in chemistry, biology, and economics, as well as in mathematics and engineering. Logarithms can be viewed as another way of writing exponents. Historically, logarithms have been used to simplify calculations; in fact, the slide rule, a device long used by engineers, is based on logarithmic scales. In the present world of inexpensive hand calculators, the need for manipulating logarithms is reduced. The function f(x) = 2x is very different from any of the functions. However, f(x) = 2x has a variable in the exponent and does not fall into the class of algebraic functions. Exponential functions occur in a wide variety of applied problems. The model defined by the function Q(t) = q0e−kt, k > 0 is called an exponential decay model; k is a constant, called the decay constant, and t is the independent variable denoting time. There are three fundamental properties of logarithms that have made those a powerful computational aid.