Related rates question?

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I am trying to solve the following question but I am not sure how to approach it. I know that I have to get the derivative of $s$ but how do I get the rate at which sales are currently changing?

A retail store has determined that weekly sales $s$ and weekly advertising costs $c$ (both in dollars) are related by $$s = 50000 - 330000 e^{-0.0009 c}$$Currently, the weekly advertising costs are $2000$ dollars which are increasing at a rate of $300$ dollars per week. Find the rate at which sales are currently changing.

score 0 · Answer 1 · answered Nov 27 '13 at 22:08

0

Let me rephrase your problem.

$s(t)=50000 - 330000 e^{-0...9 c(t)}$

$c(t_0)=2000$

$c'(t_0)=300$

$s'(t_0)=\,?$

Can you solve it now?

answered Nov 27 '13 at 22:08

xavierm02

7,495

How would you get the equation for c(t0)? – user1804933 Nov 27 '13 at 22:16
They tell you that the advertising costs are currently (for $t=t_0$) $2000$ ($c(t_0)=2000$) and are increasing at a rate of $300$ per week ($c'(t_0)=300$). – xavierm02 Nov 27 '13 at 23:02

Related rates question?

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