At 1:00 pm one winter afternoon, there is a power failure at your house in Wisconsin, and your heat does not work without electricity. When the power goes out, it is 72°F in your house. At 10:00 p is 53°F in the house, and you notice that it is 8° F outside. (a) Assuming that the temperature, T, in your home obeys Newton's Law of Cooling, write the differential equation satisfied by T. dT dt (Use k for any constant of proportionality in your equation; your equation may involve Tand the values in the problem. (b) Solve the differential equation to estimate the temperature in the house when you get up at 8:00 am the next morning. Temperature = Should you worry about your water pipes freezing? yes v (c) Think about your equation in (a): what assumption did you make about the temperature outside? Given this (probably incorrect) assumption, would you revise your estimate up or down? (And why?) Revise 2 dn

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