Suppose you have just poured a cup of freshly brewed coffee with temperature 94C in a room where the temperature is 20C. (a) When do you think the coffee cools most quickly? What happens to the rate of cooling as time goes by? Explain. The coffee cools most quickly as soon as it is removed from the heat source . The rate of cooling decreases towards 0 coffee approaches room temperature. since the (b) Newton's law of cooling states that the rate of cooling of an object is proportional to the temperature difference between the object and its surroundings, provided that this difference is not too large. Write a differential equation that expresses Newton's law of cooling for this particular situation. (Use t as the independent variable, y as the dependent variable, R as the room temperature, and k as a proportionality constant.) dy dt = k What is the initial condition? y(0) = = 94 In view of your answer to part (a), do you think this differential equation is an appropriate model for cooling? The answer and the model support each other because as y approaches R, dy dt approaches 0 , so the model seems appropriate.