What is the rate of change?

Question

The monthly sales of Sunny Electronics' new sound system are given by q(t) = 2,000t − 80t² units per month,

 t months after its introduction. The price Sunny charges is p(t) = 1,000 − t² dollars

 per sound system, t months after introduction. Find the rate of change of monthly sales

q'(t) =

Find the rate of change of the price.

p'(t) =

Find the rate of change of monthly revenue 5 months after the introduction of the sound system.

$___per month

Interpret your answer.

When t=  , the revenue is increasing at a rate of $  per month

Answer 1

You can use power rule to get the derivatives of sales and price easily: q^'(t) = 2,000 - 160t , p^'(t) = - 2t.

Revenue, total $ from sales, is the product of units sold and price per unit: R(t) = (2,000t - 80t²)·(1,000 - t²)

One way to get R^'(t) is to FOIL this out and apply power rule: R(t) = 80t⁴ - 82,000t² + 2,000,000

R^'(t) = 320t³ - 164,000t

R^'(5) = ...