The rate of change in the temperature of water is given by the differential dT equation =-k(T-S) where T is the temperature of the water at the dt time t (measured in hours), S the room temperature and k a positive constant. Boiling water at the temperature of 100C is left to cool down in a room temperature of 28C. It takes 1 hour for the boiling water to cool down to 82C. Show that k = In 4 3 When the temperature of the water is 60C, it is placed in the freezer of temperature -10C. Find the time taken for the water to form ice at 0C. [15 marks]