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March 26, 2017

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You pour a cup of coffee. when its poured, it is 130 F above room temperature, so we will say that difference D=130 F. 3 minutes later, it has cooled to D=117 F above room temperature. As the coffee cools, the instantaneous rate of change of D with respect to time t minutes is directly proportional to D. Write a differential equation which states this relationship.

  • Calculus AB - ,

    dT/dt = -C(T - To) ,
    where C is a positive constant and To is room tempoerature.

    C is approximately 3.3 degrees per minute per degree C, but you would have to solve the differential equation and fit the data point get the exact value of C.

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