Chapter 5.5, Problem 76E

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

     $\begin{array}{ccc}{C}^{\prime }\left(t\right)=3& and& R^{\prime }\left(t\right)\end{array}=15e^{-0.1t}$

where t is the number of years that the mine has been in operation. Find the useful life of the mine, to the nearest year. What is the total profit accumulated during the useful life of the mine?