In Exercises 13 through 16, modify the least-squares procedure as illustrated in Example 7.4.4 to find a curve of the form y = Ae^mx that best fits the given data.

(5, 33.5), (10, 22.5), (15, 15), (20, 10), (25, 6.8), (30, 4.5)

Data from Example 7.4.4.

A manufacturer gathers these data relating the level of production x (hundred units) of a particular commodity to the demand price p (dollars per unit) at which all x units will be sold:

a. Plot a scatter diagram for the data on a graph with production level on the x axis and demand price on the y axis.

b. Notice that the scatter diagram in part (a) suggests that the demand function is exponential. Modify the least-squares procedure to find a curve of the form p = Ae^mx that best fits the data in the table.

c. Use the exponential demand function you found in part (b) to predict the revenue the manufacturer should expect if 4,000 (x = 40) units are produced.

Production x (hundred units) Demand Price p (dollars per unit) 743 539 308 207 128 73 6 10 17 22 28 35