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 d t d t = k ( t − a ) dtdt=k(t-a), where t t is the temperature of the object after t t units of time have passed, a a is the ambient temperature of the object's surroundings, and k k is a constant of proportionality. suppose that a cup of coffee begins at 178 178 degrees and, after sitting in room temperature of 70 70 degrees for 13 13 minutes, the coffee reaches 172 172 degrees. how long will it take before the coffee reaches 157 157 degrees?