A cool drink is removed from a refrigerator on a hot summer day and placed in a room whose temperature is 30 Celsius. According to Newton’s law of cooling, the temperature of the drink t minutes later is given by a function of the form f(t) = 30 − Ae^−kt. Show that the rate of change of the temperature of the drink with respect to time is proportional to the difference between the temperature of the room and that of the drink.