Newton\'s law of cooling states that the temperature of an object changes at a r

Question

Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. If the coffee has a temperature of 200 degrees Fahrenheit when freshly poured, and 2.5 minutes later has cooled to 187 degrees in a room at 72 degrees, determine when the coffee reaches a temperature of 157 degrees.
The coffee will reach a temperature of 157 degrees in             minutes.

I need the solution for this problem with the same numbers. Thanks

Explanation / Answer

-dT/dt = k (T-Ta) By using integration, T = Ta + (Tb-Ta) e^-kt Where Ta = Ambient temperature Tb = Body Initial temperature K= proportionality constant First we have to calculate the value of k by using initial data, which is found to be 7.14*10^-4 Now calculate the value of time for a temperature of 157 degrees, Time = 9.55minutes.

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