College Algebra & Trigonometry, 2018a

Chapter 3
Exponents and Logarithms
In this chapter, we will examine concepts that are related to exponential, logarithmic
and logistic relationships. In the first section, we will look at how to approach
these problems from a graphical perspective. In the subsequent sections, we will
examine the methods necessary to work with these problems algebraically.
3.1 Exponential and Logistic Applications
There are a variety of different types of mathematical relationships. The simplest
mathematical relationship is the additive relationship. This is a situation in which
the value of one quantity is always a certain amount more (or less) than another
quantity. A good example of an additive relationship is an age relationship. In
an age relationship, the age of the older person is always the same amount more
than the age of the younger person. If the older person is five years older, then
the age of the older person (y) will always be equal to the age of the younger
person (x) plus five: y = x +5.
Another type of additive relationship is seen where two quantities add up to a
constant value. Let’s say there is a board whose length is 20 inches. If we cut
it into two pieces, with one piece being 6 inches, then the other piece will be 14
inches. If one piece is 9 inches, then the other will be 11 inches. If one piece is x
inches, then the other piece (y) will be 20 − x: y =20− x or x + y =20.
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