A large tank has a leak and the rate of change of the volume in the tank is given Question 18 by dV -kV? dt where t is time in minutes. Initially, the tank has 500 litres of water in it. 500 (a) Solve the differential equation and show that V = 1+ 500kt 1 (b) One minute later, a tenth of the water had leaked out. Show that k 4500 (c) Hence, find how long it takes for three quarters of the total water to leak out?

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