Answer to Question #212566 in Calculus for Akhona Klanisi

Question

Q 10

A tool hiring company has estimated that the rate of increase in the maintenance cost of power drills is given by the equation

C(t) = 2 + t^1,5,

where t is the time that the company is in operation for weeks. Calculate the total maintenance cost during the first four weeks.

 

1.      10

2.      22.36

3.      20.8

4.      32.36

Answer 1

$C(t) = 2 + t^{1.5}$

Total maintenance cost during the first four weeks:

$TMC = \int^4_0 (2 + t^{1.5} )dt\\ TMC = 2t + \frac{t^{2.5}}{2.5} \\ t = 4 \\ TMC = 2 \times 4 + \frac{4^{2.5}}{2.5} \\ = 8 + 12.8 = 20.8$

Answer: [3] 20.8