The rate of change of temperature with respect to time of a body is proportional to minus the difference between the temperature of the body and its surroundings.
Suppose that the room temperature is and we pour boiling water from a kettle into a cup. At time seconds later, let be the difference between the water temperature in the cup and the room temperature, and suppose that the rate of cooling is . For how long do we need to wait until the coffee is drinkable at ?