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Newton's law of cooling is: du/dt = -k (u-T) where u(t) is temperature of an object,...

Newton's law of cooling is: du/dt = -k (u-T) where u(t) is temperature of an object, t is in hours, T is a constant ambient temperature, and k is a positive constant.

Suppose a building loses heat in accordance with Newton's law of cooling. Suppose that the rate constant k has the value 0.15 hr^-1 . Assume that the interior temperature is Ti = 77F, when the heating system fails. If the external temperature is T = 5F, how long will it take for the interior temperature to fall to T1 = 35F?

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