4 Exponential and Logarithm Functions
The exponential function is one of the most important in engineering. It describes behaviour
that is of a rapidly increasing or decreasing nature – for example bacterial growth or
radioactive decay. Yet the exponential function is found to be one of the most troublesome
for newcomers to engineering mathematics. This chapter therefore introduces the key ideas
quite gently.
Prerequisites
It will be helpful if you know something about:- powers and indices (70
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) - plotting graphs (91
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) - irrational numbers (6
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) - binomial theorem (106
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)- inverse of a function (100
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)Objectives
In this chapter you will find- functions of the formy=anwhereais given andnis an integer
- the general exponential functionax
- the natural exponential functionex
- manipulation of the exponential function
- logarithms to general basea
- manipulation of logarithms
- some applications of logarithms
Motivation
You may need the topics of this chapter for:- the exponential form of complex numbers (Chapter 12)
- solving differential equations (Chapter 15)
- modelling engineering, scientific and other situations where some quantity grows
or decays very rapidly – ‘exponentially’ - converting power laws to linear form