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Math Help - Newton's Law of Cooling Question

  1. #1
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    Question Newton's Law of Cooling Question

    A pizza, heated to a temperature of 350 degrees Fahrenheit is taken out of an oven and placed in a 75 degree room at time t = 0 minutes. The temperature of the pizza is changing at a rate of -110e^0.4t degrees Fahrenheit per minute. To the nearest degree, what is the temperature of the pizza at time t = 5 minutes?

    I am not sure if I simply have to substitute in the time of 5 minutes and add it to the original temperature of 350 degrees, I've never done a question like this before. Could anyone help me out?
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  2. #2
    Senior Member euclid2's Avatar
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    Quote Originally Posted by xxlvh View Post
    A pizza, heated to a temperature of 350 degrees Fahrenheit is taken out of an oven and placed in a 75 degree room at time t = 0 minutes. The temperature of the pizza is changing at a rate of -110e^0.4t degrees Fahrenheit per minute. To the nearest degree, what is the temperature of the pizza at time t = 5 minutes?

    I am not sure if I simply have to substitute in the time of 5 minutes and add it to the original temperature of 350 degrees, I've never done a question like this before. Could anyone help me out?
    \frac{df}{dt}=-110e^{-0.4t}

    get the antiderivative

    F(t) =  - 110 e^{-0.4t}/-0.4 + F0

    F(t) =  275 e^{-0.4t} + F0

    375 =  275(1) + F0

    F0 = 100

    Becomes;

    <br />
F(t) =  275 e^{-0.4t} + 100

    F(5) =  275 e^{-0.4}(5) + 100

    F(5) =  275 e^{-2} + 100

    I'm sure you can take it from here
    Last edited by euclid2; January 30th 2009 at 05:28 AM.
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