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In: Math

The monthly sales of Stewart Electronics' new sound system are given by q(t) = 2000t -...

The monthly sales of Stewart Electronics' new sound system are given by q(t) = 2000t - 100t² units per month, t months after its introduction. The price Stewart charges is p(t) = 1000 - t² dollars per sound system, t months after introduction.

a. Find the rate of change of monthly sales after 6 months.

b. Find the rate of change of monthly price after 6 months.

c. Find the equation of the rate of change of the monthly revenue.

d. Find the rate of change of the monthly revenue after 6 months.

Expert Solution

Answer :

The monthly sales of Stewart Electronics' new sound system are given by q(t) = 2000t - 100t² units per month, t months after its introduction.

The price Stewart charges is p(t) = 1000 - t² dollars per sound system, t months after introduction.

(a) Then q'(t) = 2000 - 200t

when t = 6 we have q'(6) = 2000 - 200(6) = 800

The rate of change of monthly sales after 6 months is 800 dollars /month.

(b) And now p'(t) = - 2t

when t = 6 we have p'(6) = - 2(6) = - 12

The rate of change of monthly price after 6 months is - 12 dollars/month.

(c) The revenue is given by R(t) = tp(t) - q(t)

R(t) = 1000t - t³ - ( 2000t - 100t² ) = - t³ - 1000t + 100t²

The equation of the rate of change of the monthly revenue is R'(t) = - 3t² - 1000 + 200t

(d) when t = 6 we have R'(6) = -3(6²) - 1000 + 200(6) = 92

The rate of change of the monthly revenue after 6 months is 92 dollars per month

milcah answered 2 years ago

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