This exercise uses Newton's Law of Cooling. Newton's Law of Cooling is used in homicide investigations to determine the time of death. The normal body temperature is 98.6F. Immediately following death, the body begins to cool. It has been determined experimentally that the constant in Newton's Law of Cooling is approximately k = 0.1947, assuming time is measured in hours. Suppose that the temperature of the surroundings is 65F.(a) Find a function T(t) that models the temperature t hours after death.

T(t) =

(b) If the temperature of the body is now 78F, how long ago was the time of death? (Round your answer to the nearest whole number.) hr