CHAPTER ELEVEN - EXPONENTIAL AND LOGARITHMIC FUNCTIONS

Abstract

The function concept can serve as a unifying idea in mathematics. Functions can be combined in a variety of ways, a few of which may be anticipated such as the addition and multiplication of two or more functions). Functions can be combined by applying one function to another to obtain a composite function. At times, it is also possible to define a function g that reverses the correspondence of a function f. An important pair of such inverse functions is that of the exponential and logarithmic functions. An inverse function off can be defined only iff is one-to-one. It is sometimes possible to find an inverse by algebraic methods. To solve an exponential equation, logarithms of both sides of the equation are taken and converted to the equivalent exponential form to solve a logarithmic equation. Exponential functions occur in a wide variety of applied problems. This chapter presents problems dealing with population growth such as that of growth of bacteria in a culture medium, radioactive decay, and interest earned when the interest rate is compounded.