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Post  Post subject: Exponential Decay Question  |  Posted: Sun Oct 02, 2011 1:31 pm
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On a recent maths homework set, I came across a question that I'm having trouble with. It says:

"A bath is filled with water at a temperature of 40°C. After t minutes the temperature has fallen to

$ \displaystyle (10 + 30e^{-0.04t})$°C."

a) Find the rate at which the temperature is falling when the temperature is 38°C.

So, I had

$ \displaystyle 10 + 30e^{-0.04t}=38$

$ \displaystyle \Rightarrow 30e^{-0.04t}=28$

$ \displaystyle -1.2t\,ln e = ln 28$

So, $ \displaystyle t = \frac{ln 28}{-1.2} = -2.7768$

The, I differentiated the equation in the question

$ \displaystyle \dfrac{dT}{dt} = -1.2e^{-0.04t}$

to obtain the rate, which I put the time calculated above into to get:

$ \displaystyle -1.2e^{-0.04(-2.7768)} = -1.341$°C/min.

However, the book states that the answer is actually -1.12°C/min. Where have I gone wrong?

Thanks in advance!

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"Nature doesn't care what we call it, she just does it anyway".
- Feynman


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Post  Post subject: Re: Exponential Decay Question  |  Posted: Sun Oct 02, 2011 2:32 pm
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Never mind, I got the answer! I forgot to divide by the 30, rookie mistake! :D

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"Nature doesn't care what we call it, she just does it anyway".
- Feynman


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