The initial value of an appliance is $700 and its value in the future is given by $\displaystyle v(t)=100(2^{3-t}-1)$, $\displaystyle 0\let\le3$, where t is time in years. Thus after the first 3 years the appliance is worth nothing as far as the warranty is concerned. If it fails in the first 3 years, the warrantee pays v(t). Compute the expected value of the payment on the warranty if T has an exponential distribution with mean 5.