A hard-boiled egg is removed from a pot of hot water and set on the table to cool. Let the temperature of the body at time t be T(t). Assume the change of the temperature of the body satisfies Newton's law of cooling: (Please see attachment).
(i) Initially, the egg's temperature is 90 degree C. After an hour its temperature is 60 degree C. Solve the differential equation and hence determine the function T in terms of t.
(ii) When will the egg's temperature be 50 degree C?