Jane McGee, the mathematics editor at a major publishing house, estimates that if x thousand complimentary copies are distributed to professors, the first-year sales of a certain new text will be f(x) = 20 − 15e^−0.2x thousand copies. Currently, Jane is planning to distribute 10,000 complimentary copies.

a. Use marginal analysis to estimate the increase in first-year sales that Jane should expect if 1,000 additional complimentary copies are distributed.

b. Calculate the actual increase in first-year sales that will result from the distribution of the additional 1,000 complimentary copies. Is the estimate in part (a) a good one?