When professors select texts for their courses, they usually choose from among the books already on their shelves. For this reason, most publishers send complimentary copies of new texts to professors teaching related courses. The mathematics editor at a major publishing house estimates that if x thousand complimentary copies are distributed, the first-year sales of a certain new mathematics text will be approximately f(x) = 20 − 15e^−0.2x thousand copies.

a. Sketch this sales function.

b. How many copies can the editor expect to sell in the first year if no complimentary copies are sent out?

c. How many copies can the editor expect to sell in the first year if 10,000 complimentary copies are sent out?

d. If the editor’s estimate is correct, what is the most optimistic projection for the first-year sales of the text?