A dam is being emptied. The amount of water remaining in the dam after t days is V = 27(243 − 3t)3 litres where t ∈ [0, 81].
(1) How many litres of water were in the dam when t = 0?
(2) When is the amount of water in the dam 729 litres?
3) What is the rate of change of V with respect to time t?
(a) Evaluate this function when t = 0
(b) Evaluate this function when t is your answer for Q2.
(c) Compare your answers for Q3(a) and Q3(b). At which of these two times was the tank emptying at a greater rate? Explain why.