Noelle W.

asked • 10/10/14

Intro To Calc Problem With Temperature

A potato is put in a hot oven at t=0. After t minutes, the temperatures is T(t)=350-280e-.2t degrees. What is the initial temperature of the potato, and what is the temperature of the oven? 
Please don't use chain rule. Thanks!!

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Francisco P. answered • 10/10/14

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The initial temperature of the potato occurs at t = 0.  T(0) = 350 - 280e-0.2(0) = 350 - 280 = 70º F.
 
The potato will reach the temperature of the oven after spending time in the oven.  Choose t = ∞ for the time to get
 
T(∞) = 350 - 280e-0.2(∞) = 350º F.
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Noelle W.

Hmmm... I see what you did there, but .2t was not an exponent of 280e. And why were you able to use infinity to reach the oven temperature? Does it have something to do with a limit? 
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10/10/14

Francisco P.

I think it should be there.  Could you recheck the wording of the problem?
 
I used infinity to represent a long time--enough time that the temperature of the potato is essentially that of the oven.  A decaying exponential function is asymptotic to zero.
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10/10/14

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