Suppose that a tank initially contains 80 litres of pure water. At a given instant (taken to be t = 0) a salt solution containing 0.25 kg of salt per litre flows into the tank at a rate of 8 litres min^–1. The liquid in the tank is kept homogeneous by constant stirring. Also, at time t = 0 liquid is allowed to flow out from the tank at a rate of 12 litres min^–1. Show that the amount of salt x(t) (in kg) in the tank at time t (min) ≥ 0 is determined by the mathematical model

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dx(t) dt + 3x(t) 20 - t = 2 (t <20)