A cup of hot chocolate is initially 170° F and is left in a room with an ambient temperature of 70° F. Suppose that at time t = 0 it is cooling at a rate of 20° per minute.
(a) Assume that Newton’s law of cooling applies: The rate of cooling is proportional to the difference between the current temperature and the ambient temperature. Write an initial-value problem that models the temperature of the hot chocolate.
(b) How long does it take the hot chocolate to cool to a temperature of 110° F?
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