You spend winter break somewhere cold. One night, when the temperature in your house is 70 F and the outside temperature is 20 F, the heat in your house fails. Two hours later, the temperature inside the house has fallen to 50 F. Assume that the outside temperature remains at 209F. A. Recall that Newton's law of cooling states that the rate of change of temperature is proportional dT to the temperature differential: k(T - Tm ) . Use Newton's law of cooling to set up an initial dt value problem modeling the rate of change of temperature. B. Solve the IVP in part A. C. How long does it take for the temperature inside the house to fall to 40 F? Give an exact answer in terms of logarithms. Type your answers into the box below and be sure to upload your work to the "Upload 5 Work"