Question 3. After a murder has been committed, the body. which was originally at 37C, cools according to Newton's Law of Cooling: for some positive constant k. the rate of change of its temperature is proportional to the temperature difference with the ambient air. We will suppose that. after 1.5 hours. the temperature of the body. B, is 34.5C. while the surrounding temperature of the ambient air is 18C. a) Write down the differential equation governing the change of the body temperature B with time, t, in terms of k. b) Find the temperature B of the body as a function of k. the time t (in hours) after the murder was committed, and an arbitrary constant A. c) Determine the values of A and it from the information given, showing your calculation clearly. d) Sketch a graph of the body temperature B against time t. e) What happens to the body temperature B in the long run? Consider the limit of your solution and comoare to vour graph