Question

Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 + 0.005x2 + 28x + 3000. (a) Find the average rate of change of total cost when production changes from 300 to 500 printers. (b) Find the average rate of change of total cost when production changes from 500 to 700 printers. (c) Interpret the results from parts (a) and (b).

Answer 1

Answer:a) 52.68%

b) 48.18%

Step-by-step explanation: [Tex]c= 0.0001x^3 + 0.005x^2 + 28x + 3000[/Tex]

a) to get rate of change from 300 to 500, substitute 300 as x in the formular then get 14550, also substitute 500 as x in the formular to get 30750 then do rate as [Tex](30750-14550)/30750 x 100% = 52.68%

b) to get rate of change from 500 to 700, substitute 700 in the formular to get 59350 to get 59350, we already have 30750 after substituting 500 in the formular previously, so rate = [Tex](59350-30750)/59350 [/Tex] x 100% = 48.18%. the significance of this answer is that, the more printer you produce the smaller the rate of change in cost.