A cup of tea at 90 °C is placed in a room whose constant temperature is 25 °C. Ten minutes later, the temperature of the tea is 70 °C. The rate of cooling is proportional to the difference between the temperature of the tea and the room.
(i) Frame the differential equation satisfied by the temperature T(t) (in °C) of the tea t minutes after it is placed in the room and write its general solution.
(ii) Determine the cooling constant k (correct to four decimal places).
(iii) Find the temperature of the tea 20 minutes after it is placed in the room.
(iv) After how many minutes from the start will the temperature of the tea reach 40 °C? (Answer correct to one decimal place.)