Chapter 5.2, Problem 82E

Marketing. Repeat Problem 81 if the monthly rate of increase in sales is found to be approximated by

     $\begin{array}{cc}{S}^{\prime }\left(t\right)=20-20e^{-0.05t}& 0\le t\le 24\end{array}$

81. Marketing. An automobile company is ready to introduce a new line of hybrid cars through a national sales campaign. After test marketing the line in a carefully selected city, the marketing research department estimates that sales (in millions of dollars) will increase at the monthly rate of

     $\begin{array}{cc}{S}^{\prime }\left(t\right)=10-10e^{-0.1t}& 0\le t\le 24\end{array}$

t months after the campaign has started.

(A)    What will be the total sales S(t) t months after the beginning of the national campaign if we assume no sales at the beginning of the campaign?

(B)    What are the estimated total sales for the first 12 months of the campaign?

(C)    When will the estimated total sales reach $100 million? Use a graphing calculator to approximate the answer to two decimal places.