A product is introduced to the market. The weekly profit (in dollars) of that product decays exponentially as function of the price that is charged (in dollars) and is given by P(x) = 85000 · e-0.04.x Suppose the price in dollars of that product, ä(t), changes over time t (in weeks) as given by x(t) = 49 +0.81 · t² Find the rate that profit changes as a function of time, P'(t) How fast is profit changing with respect to time 4 weeks after the introduction. dollars/week dollars/week
A product is introduced to the market. The weekly profit (in dollars) of that product decays exponentially as function of the price that is charged (in dollars) and is given by P(x) = 85000 · e-0.04.x Suppose the price in dollars of that product, ä(t), changes over time t (in weeks) as given by x(t) = 49 +0.81 · t² Find the rate that profit changes as a function of time, P'(t) How fast is profit changing with respect to time 4 weeks after the introduction. dollars/week dollars/week
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A product is introduced to the market. The weekly profit (in dollars) of that product decays exponentially as function of the price that is charged (in dollars) and is given by �(�)=85000⋅�-0.04⋅�
Suppose the price in dollars of that product, �(�), changes over time � (in weeks) as given by �(�)=49+0.81⋅�2
Find the rate that profit changes as a function of time, �′(�) dollars/week
How fast is profit changing with respect to time 4 weeks after the introduction. dollars/week
Transcribed Image Text:A product is introduced to the market. The weekly profit (in dollars) of that product decays exponentially
as function of the price that is charged (in dollars) and is given by P(x) = 85000.e-0.04.
Suppose the price in dollars of that product, ä(t), changes over time t (in weeks) as given by
x(t) = 49 +0.81 · t²
Find the rate that profit changes as a function of time, P'(t)
How fast is profit changing with respect to time 4 weeks after the introduction.
dollars/week
dollars/week
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