Question: A recently installed machine earns the company revenue at a continuous rate of \(60,000t+45,000\) dollars per year during the first six months of operation and at the continuous rate of 75,000 dollars per year after the first six months. The cost of the machine is $150,000, the interest rate is 7% a year, compounded continuously, and t is the time, the number of years since the machine was installed

(a) Find the present value of the revenue earned by the machine during the first year of operation

(b) Find how long it will take for the machine to pay for itself.