Use the diagnostic feature of your graphing calculator to determine if the following data can be modelled by an exponential function. If it can, write the exponential regression function, and graph the function on the same grid as the data set.

x
0
1
2
3
4
5
6
7
y
20
21.46
22.99
24.64
26.43
28.33
30.35
32.56

Note: You do not need to turn on the STAT PLOT to find the regression equation or the coefficient of determination. To find the regression equation only, omit steps 1, 2, 3, and 7.

Step 1: Turn on the STAT PLOT; press 2nd, Y=, ENTER, ENTER.

Step 2: Clear the functions; press Y= then, CLEAR for each function that needs deleting.

Step 3: Select values for the viewing window; press WINDOW.

Step 4: Go to the lists; press STAT, ENTER.

Step 5: Clear the lists; press the up arrow until the column heading is highlighted; then, press CLEAR, ENTER. Repeat for all columns that have unneeded data.

Step 6: Enter the data.

Step 7: View the data; press GRAPH.

Step 8: Choose the regression model; press STAT, right arrow.

Step 9: Select linear regression; press 4, ENTER. Repeat Steps 8 and 9 for exponential regression.

Compare the R2 values. Exponential regression has the highest R2; therefore, it is the best model for this data.

Step 10: Place the exponential regression into the function area; press STAT, right arrow, 0, VARS, right arrow, ENTER, ENTER, ENTER.

Step 11: View the scatter plot and regression model; press GRAPH.

The exponential regression, rounded to two decimal places, is y = 20.01(1.07)x.

Complete the questions on page 377 (1a, 1b and 1c) for practice determining if the data can be modelled by an exponential function.

Click here to verify your answers.