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Math Help - [SOLVED] Cal2 Integral Word Problem (finding average)?

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    [SOLVED] Cal2 Integral Word Problem (finding average)?

    (a) A cup of coffee has temperature 95 C and takes 30 minutes to cool to 61 C in a room with temperature 20 C. Use Newton's Law of cooling system to show that the temperature of the coffee after t minutes is
    T(t) = 20 + 75e^(-kt) where k = 0.02

    (b) What is the average temperature of the coffee during the first half hour?
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  2. #2
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    Quote Originally Posted by racewithferrari View Post
    (a) A cup of coffee has temperature 95 C and takes 30 minutes to cool to 61 C in a room with temperature 20 C. Use Newton's Law of cooling system to show that the temperature of the coffee after t minutes is
    T(t) = 20 + 75e^(-kt) where k = 0.02

    (b) What is the average temperature of the coffee during the first half hour?
    (a) Newton's law of cooling says the rate at which a substance cools is directly proportional between the temperature of the substance and the temperature of its surroundings.

    \frac{dT}{dt} = -k(T - S)

    solve the differential equation for T using the given time/temp data.

    (b) T_{avg} = \frac{1}{t_2 - t_1} \int_{t_1}^{t^2} T(t) \, dt
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    can tell me what is the value of T and S and how what values to be put in the equation

    Thanks
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  4. #4
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    Quote Originally Posted by racewithferrari View Post
    can tell me what is the value of T and S and how what values to be put in the equation

    Thanks
    S = 20 ... T is a variable
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