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5 The temperature of a cup of coffee on the counter is initially at 95C and is left in a room with surrounding temperature 25C.

5 The temperature of a cup of coffee on the counter is initially at 95C and is left in a room with surrounding temperature 25C. The temperature, 'C, of the hot coffee at time & minutes is given by the differential equation de dt = -k(0-5), where k is a constant, is the temperature of hot coffee and S is the room temperature. (a) By separating the variables, express in terms of k and r. [4 marks] (C3, CLO3, MQF LOD 6) (b) Suppose that when the hot coffee is first place in the room, it cools down to 65C in 10 minutes. Solve the differential equation to find in terms of t. KALJ [3 marks] (C3, CLO3, MQF LOD 6) (c) How long does it take for the hot coffee to cool from 65C to 40C? [3 marks] (C3, CLO3, MQF LOD 6) END OF QUESTIONS

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