in a room where the temperature is 20 C 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 Select 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 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 What is the initial condition y 0 In view of your answer to part a do you think this differential equation is an appropriate model for cooling Select dy dt approaches Select The answer and the model 974 c Make a rough sketch of the graph of the solution of the initial value problem in part b y 20 because as y approaches R The rate of cooling Select towards Select since the coffee approaches room temperature t DO y 979 so the model seems appropriate o 774 779 20