Suppose that a 200°F freshly poured cup of coffee is placed in a large room which has an ambient temperature of 72°F and immediately forgotten about. (a) Set up an initial value problem whose solution is Y(t), the temperature of the cup of coffee (in degrees Fahren- heit) t minutes after it was poured. (Hint: we don't know the rate of proportion of the cup of coffee, so feel free to call it whatever you want.) (b) Suppose after one minute, the coffee has reached a temperature of 190°F. Use this information to determine the rate of proportion of cooling. (c) Clearly state Y(t), the function which models the temperature of the cup of coffee t minutes after it's been poured. (d) How long does it take for the temperature of the coffee to be within 5% of the ambient temperature?

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