Arecently-installed machine earns the company revenue at acontinuous rate of 60,000t + 45,000 dollars per year during thefirst six months of operation and at the continuous rate of 75,000dollars per year after the first six months. the cost of themachine is $150,000, the interest rate is 7% per year, compoundedcontinuously, and t id time in years since the machine wasinstalled.(a) find the present value of the revenue earned by themachine during the first year of operation.(b) find how long it will take for the machine to pay foritself; that is, how long will it take for the present valueof the revenue to equal the cost of the machine?