Mathematics for Electrical Engineering and Computing

8

The exponential function

8.1 Introduction

In Example 2.11, we looked at an acoustical absorption problem. We found that after a single note on a trombone had been played, the sound intensity decayed according to the expression I = 10^−11t. This is a dying exponential function. Many other physical situations involve decay or growth in an exponential fashion; for instance, population growth or the decay of charge on a discharging capacitor. The functions y = a^t, where a can be any positive number, are called exponential functions. In this chapter, we shall look at how they describe this particular type of growth or decay, when the growth or decay is proportional to the current size of the ‘population’, y. This situation can be described by a differential ...