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A thermometer is taken from a room where the temperature is 24C to the outdoors, where the temperature is -10C. After one minute the thermometer reads 13"C. (a) What will the reading on the thermometer be after 5 more minutes? (b) When will the thermometer read 0C? minutes after it was taken to the outdoors. 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 205 degrees Fahrenheit when freshly poured, and 2.5 minutes later has cooled to 189 degrees in a room at 64 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. de T(0) = (b) Solve the initial value problem in part (a). Your answer will contain the unknown constant k. T() - (c) Determine the value of the constant k K- (d) Determine when the coffee reaches a temperature of 159 degrees. minutes. Note: You can earn partial credit on this problem. Preview My Answers Submit Answers You have attempted this problem 2 times. Your overall recorded score is 40% A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the rate 4 L/min. (a) Write an initial value problem for the amount of salt, y. in kilograms, at time t in minutes: dy at -(kg/min) y(0) -kg (D) Solve the initial value problem in part (a) y (t) - kg (c) Find the amount of salt in the tank after 3.5 hours. amount - (kg) (d) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration = | (kg/L) Note: You can earn partial credit on this