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A New View on Exponential Functions

In one of the modules in this course, you examine the properties and characteristics of exponential functions. The general form of the exponential function is:

 

f of x equals a times b to the x power

 

where a is the leading coefficient and b is the base to which the variable exponent is applied.

When you create a table of values for exponential functions, you may identify a pattern. Consider the function

 

f of x equals 3 times 2 two to the x power

 

A table of values, for x values consisting of some positive integers, is as follows:

Table of values
x f(x)
1 6
2 12
3 24
4 48
5 96

Do you see a pattern? Each successive term is the preceding term multiplied by the base. These function values, produced when the domain is limited to the positive integers, constitute a sequence with a distinct pattern: each term is determined by multiplying the preceding term by the base.

In the next topic, we will examine sequences with the pattern of a constant multiplier between terms. These sequences are called geometric sequences, and the constant multiplier is called the common ratio.


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