The temperature, T °C, of a cup of tea is given by T = 55 e^−t/8 + 20 t ≥ 0 where t is the time in minutes since measurements began.

a. Briefly explain why t ≥ 0.

b. State the starting temperature of the cup of tea.

c. Find the time at which the temperature of the tea is 50°C, giving your answer to the nearest minute.

d. By sketching a graph or otherwise, explain why the temperature of the tea will never fall below 20 °C.