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Newton's Law of Cooling tells us that the rate of change of the temperature of an...

Newton's Law of Cooling tells us that the rate of change of the temperature of an object is proportional to the temperature difference between the object and its surroundings. This can be modeled by the differential equation dTdt=k(T−A)dTdt=k(T-A), where TT is the temperature of the object after tt units of time have passed, AA is the ambient temperature of the object's surroundings, and kk is a constant of proportionality.

Suppose that a cup of coffee begins at 179179 degrees and, after sitting in room temperature of 6060 degrees for 1212 minutes, the coffee reaches 170170 degrees. How long will it take before the coffee reaches 155155 degrees?

Include at least 2 decimal places in your answer.

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