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Math Help - Newtons law of cooling problem

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    Newtons law of cooling problem

    I need help setting up the following problem.

    A freshly brewed cup of coffee has temperature 95 degrees C in a 20 degree C room. When its temperature is 73 degrees C, it is cooling at a rate of 1 degree C per minute. When does this occur?
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    Quote Originally Posted by izzychec View Post
    I need help setting up the following problem.

    A freshly brewed cup of coffee has temperature 95 degrees C in a 20 degree C room. When its temperature is 73 degrees C, it is cooling at a rate of 1 degree C per minute. When does this occur?
    Newton's law of cooling states that the rate of cooling is proportional to the temperature difference between the coffee and its environment.

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

    where T is the coffee's temperature at any time t and E is the temperature of the environment.

    you were given the rate of cooling at T = 73 ... you should be able to find the proportion constant k using that info.

    once you do, separate variables and solve for T as a function of t and solve the problem.
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