Chapter 5.5, Problem 75E

Useful life. The total accumulated costs C(t) and revenues R(t) (in thousands of dollars), respectively, for a photocopying machine satisfy

     $\begin{array}{ccc}{C}^{\prime }\left(t\right)=\frac{1}{11}t& and& R^{\prime }\left(t\right)=5t{e}^{-r^2}\end{array}$

where t is time in years. Find the useful life of the machine, to the nearest year. What is the total profit accumulated during the useful life of the machine?