### 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^{prime}(t)=(9 t+15) sqrt{1.5 t^{2} pm 5 t} text {, for } 0 leq t leq 10, ] where ( C ) is the maintenance cost in dollars and ( t ) is the number of years

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^{prime}(t)=(9 t+15) sqrt{1.5 t^{2} pm 5 t} text {, for } 0 leq t leq 10, ] where ( C ) is the maintenance cost in dollars and ( t ) is the number of years