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