A recently installed machine earns the company revenue at a continuous rate of 60000t + 45,000 dollars per yr during the first six months of operation and at a continous rate of 75000 dollars per yr after the first six months. The cost of the machine is $150,000, interest rate is 7% compounded continuously and t is the time in years since it was installed.
a.) Find present value of revenue earned by machine during first yr of operation
b.) Find how long it will take the machine to pay for itself, how long will it take for the present value of the revenue to equal the cost of the machine?