2- (20 points) Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between the temperature of the object itself and the temperature of its surroundings. Suppose that a building loses heat in accordance with Newton's law of cooling and that the rate constant k has the value of 0.15 hr. a) Write a differential equation for the interior temperature of the building at any time. Assume that the interior temperature is 20°C when the heating system fails. If the external temperature is -10°C, b) How long will take for the interior temperature to fall to 0°C.