13. [12 marks] A cook has finished baking a cake and placed it on the bench to cool. The temperature in the room is 25C and the temperature of the cake when it was taken out of the oven is 170C (a) Given that the temperature of the cake is governed by Newton's law of cooling, write down a differential equation governing T(t), the temperature of the cake after t hours. What is the appropriate initial condition? (Newton's law of cooling: dT dt = -K(T - Ta), where K is a constant and To is the ambient temperature.) (b) From you answer in part (a), derive the solution T(t) = 25 + 145e-Kt, At, where K is a constant