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The amount of water in a tank $t$ minutes after it has started to drain is given by $W = 100t^2 - 3000t + 22500$ where $W$ is measured in gallons.

At what rate is the water running out at the end of $5$ minutes?

I know the process to get the answer: simply derive the function to get the flow function and then plug 5 minutes into that. Doing this gets the answer $-2000 \frac{\text{gal}}{\text{min}}$, and that is the slope of the volume function at 5 minutes. However, I believe that the answer is positive $2000 \frac{\text{gal}}{\text{min}}$ because the question is asking what rate the water is flowing OUT.

I want to know which answer would be right on the AP test. I have tried to find a similar problem on one of the sample tests, but I can only find ones that give a rate water is draining (which is positive) and have you find the volume. Thanks!

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    $\begingroup$ I think $+$ is better but a case might be made for either $+$ or $-$. This isn't really a math question, but an English question. $\endgroup$ – vadim123 Sep 18 '13 at 22:45
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It's running out of the tank at $2000$ gallons per minute.

The rate of change of volume with respect to time is $-2000$ gallons per minute.

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