CALCULUS FOR BUSINESS

Question

Based U.S. Postal Rate data from 1932-2014, the cost (in cents) to mail a single letter is modeled by the function: C(t) = 0.007714t^2 − 0.039695t+ 0.726

where t is the number of years since 1932.

a. Using this model, what was the cost of mailing a single letter in 1982?

b. How fast will the cost of mailing a single letter be changing in 2017? Is the cost rising or falling?

Answer 1

a. In 1982 time t = 1982 - 1932 = 40 years

C(40) = 0.007714·40² - 0.0396695·40 + 0.726 = 11.48 cents

b. C'(t) = 0.015428t - 0.039695. In 2017 t = 2017 - 1932 = 85;

C'(85) = 0.01528·85 - 0.039695 = 1.259105 cents/year > 0. So, cost increasing.