Watch the Creating Exponential Graphs video to see a demonstration of the calculator steps for constructing an exponential function.

Example 1 states explicitly to use an exponential regression model for the data. In most problems, this information is not given. Typically, you must plot the given data, view the scatter plot, and use your knowledge of functions to select the regression model that best fits the data points. If the scatterplot does not give a clear indication that the data is exponential, you can check using the method shown in Example 2.

Determine if each of the following sets of data represent exponential growth or decay.

a.
x
2
3
4
5
6
7
y
32
80
200
500
1250
3125

b.
x
-3
-2
-1
0
1
2
y
20
10
5
2.5
1.25
0.625

c.
x
1
2
3
4
5
6
y
200
100
75
50
35
7

An exponential function has a constant rate of change. To confirm that a set of data represents an exponential function, you must determine if this constant rate of change exists.

Because the constant rate of change for this data is greater than one, this data represents exponential growth.

Because the constant rate of change for this data is between zero and one, this data represents exponential decay.