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 , where is the temperature of the object after units of time have passed, is the ambient temperature of the object's surroundings, and is a constant of proportionality. suppose that a cup of coffee begins at degrees and, after sitting in room temperature of degrees for minutes, the coffee reaches degrees. how long will it take before the coffee reaches degrees?