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⋅�2Find the rate that profit changes as a function of time, �′(�) dollars/weekHow fast is profit changing with respect to time 4 weeks after the introduction. dollars/week A product is introduced to the market. The weekly profit (in dollars) of that product decays exponentiallyas 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 byx(t) = 49 +0.81 · t²Find 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/weekdollars/week

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Answered: A product is introduced to the market.…

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