1. Suppose a dead body was found in a closed room of a house where the temperature was kept at a constant Tm = 70°F. Also assume that the dead body cools according to Newton's law of cooling given by the following ODE: dT dt = k (T − Tm), where T (t) is the body temperature at time t, Tm is the ambient room temperature, and k is a constant of proportionality. (a) At the time of discovery, the core temperature of the body was 80°F and one hour later the core temperature was measured to be 75°F. Let t = 0 be the time of death, and assume the body had a core temperature of 98.6°F at the time of death. How much time has passed since the person died? (Hint: rst solve the general ODE. Then use the given data to solve for the constant k in the ODE and the constant C in your general solution solution.) (b) Suppose the person had a fever of 102°F at the time of death. Now how much time do you determine has passed since death?