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

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Basic Math

Newton's Law of Cooling tells us that the rate of change of thetemperature of an object is proportional to the temperaturedifference between the object and its surroundings. This can bemodeled by the differential equation d T d t = k ( T − A ) , whereT is the temperature of the object after t units of time havepassed, A is the ambient temperature of the object's surroundings,and k is a constant of proportionality. Suppose that a cup ofcoffee begins at 188 degrees and, after sitting in room temperatureof 65 degrees for 16 minutes, the coffee reaches 181 degrees. Howlong will it take before the coffee reaches 168 degrees? Include atleast 2 decimal places in your answer.

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