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A pot of stew is placed on a stove to heat. The temperature of the liquid reaches 170°F, and then the pot is taken off the burner and placed on a kitchen counter. The temperature of the air in the kitchen is 76°F.

If k = 0.34, the temperature of the liquid after 7 hours will be ºF. (Hint: Use Newton’s cooling model.)

Respuesta :

With the given hint to be able to answer the question above, the equation for Newton's law of cooling is as follows:
                         T(t) = T(s) + (T0 - Ts)e^-kt
where T(t) is the body's temperature at any given time, Ts is the temperature of the surrounding, T0 is the initial temperature, and k is constant. 
Substituting the values with the given above,
                             T(t) = 76 + (170 - 76)*e^(-0.34)(7)
This gives us the answer,
                                     T(t) = 84.7 degrees F

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