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Math Help - Differential Equation - Newton's Law Of Cooling?

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    Differential Equation - Newton's Law Of Cooling?

    I have a homework problem I'm not sure about.

    At 6:00 pm a 50 degree drink is pulled from the refrigerator into a room that is 72 degrees. Three minutes later, at 6:03, the drink is now 53 degrees. How long, in minutes, will it be until the drink is 70 degrees?
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    Quote Originally Posted by xvaliant View Post
    I have a homework problem I'm not sure about.

    At 6:00 pm a 50 degree drink is pulled from the refrigerator into a room that is 72 degrees. Three minutes later, at 6:03, the drink is now 53 degrees. How long, in minutes, will it be until the drink is 70 degrees?
    \frac{dT}{dt} = k(72 - T)

    T(0) = 50

    T(3) = 53

    solve the differential equation using the given conditions.
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    ok, I integrated both sides an got ln(72-T)=kt. I'm confused as how to find the constant, k.
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    Quote Originally Posted by xvaliant View Post
    ok, I integrated both sides an got ln(72-T)=kt. I'm confused as how to find the constant, k.
    where is your constant of integration?
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    (72-T)=C(1) e^kt
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  6. #6
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    Quote Originally Posted by xvaliant View Post
    (72-T)=C(1) e^kt
    use T(0) = 50 to find C_1

    use T(3) = 53 to find k
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  7. #7
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    Got it. Thanks!
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