Mathematics

Laney

15 June, 04:00

As machines get older, the cost of maintaining them tends to increase. Suppose for a particular machine, the rate at which the maintenance cost is increasing is approximated by the function C' (t) = (20t+24) √ (2.5t^2+6t) for 0≤t≤150≤t≤15

where C is the maintenance cost in dollars and tt is the number of years since the purchase. The company will sell or scrap the machine in 15 years and buy a new one if the cost to maintain it in its last year of service is projected to exceed $7,750. Round all answers to the nearest cent.

a. What is the total expected cost to maintain this machine over its first 3 years of service?

b. What is the total expected cost to maintain this machine in its last year of service?

c. How many times more expensive is it to maintain the machine in its last year of service than its first year of service? Round your answer to the nearest tenth.