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(1 point) Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. Suppose that the temperature of a cup of coffee obeys Newton's law of cooling. Let k > 0 be the constant of proportionality. Assume the coffee has a temperature of 195 degrees Fahrenheit when freshly poured, and 1 minutes later has cooled to 175 degrees in a room at 66 degrees. (a) Write an initial value problem for the temperature T' of the coffee, in Fahrenheit, at time t in minutes. Your answer will contain the uknown constant k: T(0) = (b) Solve the initial value problem in part (a). Your answer will contain the unknown constant k T(t) = (c) Determine the value of the constant k k = minutes. (d) Determine when the coffee reaches a temperature of 145 degrees. minutes