Math Problem Statement
The monthly sales of Sunny Electronics' new sound system are given by q(t) = 2,000t − 100t^2 units per month, t months after its introduction. The price Sunny charges is p(t) = 1,000 − t^2 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.
Solution
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Math Problem Analysis
Mathematical Concepts
Differentiation
Revenue Functions
Rate of Change
Formulas
q(t) = 2,000t - 100t^2
p(t) = 1,000 - t^2
R(t) = p(t) * q(t)
Theorems
Product Rule of Differentiation
Chain Rule
Suitable Grade Level
Grades 11-12
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