A metal cube is dropped into a tank of water, the temperature of which is held at 17°. The initial temperature of the cube is 70°, and after 10 minutes the temperature of the cube has dropped to 35°. Assume that Newton's law of cooling applies. (i) Write down the differential equation for the temperature of the cube, T(t). (ii) What will the temperature of the cube be after 55 minutes? (iii) Will the temperature of the cube ever reach 9°? Justify your answer. (iv) What is the initial rate of change of the temperature of the cube?

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