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Question: Newton's law of cooling. Newton's law of cooling (and warming) states that the rate of change of temperature u = u(t) of an object is proportional to the temperature difference between the object and its surroundings, where T is the constant temperature of the surroundings. That is,

du/dt = k(u - T)

Suppose an object at 0°C is placed in a room where the temperature is 20°C. If the temperature of the object is 8°C after 1 hour, how long will it take for the object to reach 18°C?

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