Chapter 5.5, Problem 6MP

Matched Problem 6 Repeat Example 6 if C′(t) = 1 and $R\prime \left(t\right)=\text{ 7}\text{.5}{e}^{-0.5t}$.

EXAMPLE 6 Useful Life An amusement company maintains records for each video game installed in an arcade. Suppose that C(t) and R(t) represent the total accumulated costs and revenues (in thousands of dollars), respectively, t years after a particular game has been installed. Suppose also that

     $\begin{array}{cc}C\prime \left(t\right)=2& R\prime \left(t\right)=\text{ 9}{e}^{-0.5t}\end{array}$

The value of t for which C′ (t) = R′(t) is called the useful life of the game.

1. (A) Find the useful life of the game, to the nearest year.
2. (B) Find the total profit accumulated during the useful life of the game.