Graphs of Exponential Functions

exponential base a

3.95

multiplicative constant C

0.5

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A general exponential function has the form

f(x)=C

x

a

, where

C

and

a

are positive real numbers. The number

a

is called the exponential base and the number

C

is called the multiplicative constant.

If the base

a>1

, then the function is one of exponential growth and the function is always increasing. If the base

a<1

, then the function is one of exponential decay and is therefore always decreasing.