Chapter 19
EXPONENTIAL FUNCTIONS
This chapter explores exponential functions, inverses of logarithmic func-
tions. Specifically, f(x) = a
x
and g(x) = log
a
x are inverse functions (assuming
a > 0 and a ≠ 1). Therefore, you can use logarithms to solve exponential
equations (and vice versa). The chapter concludes with an investigation of
exponential functions used to model growth and decay.
In Chapter 18, you learn that log
6
36 = 2 because you have to raise the
base of the log (6) to the second power to get 36. It’s easier to understand
how logs work when you think of them in terms of exponents, and that’s
no accident. Logarithmic and exponential functions are actually inverses
when their bases match. For example, the inverse of f(x) = log
6
x is
.
This chapter begins a lot like Chapter 18, by exploring the graphs of
exponential functions. Then it moves into composing the inverse functions—
taking the log of an exponential function and vice versa—and applies
that to solving exponential and logarithmic equations. It ends with
exponential growth and decay, which uses the formula f(t) = Ne
kt
.
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