A vessel forms part of a water purification system. A mixture of water and pollutant flows...

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A vessel forms part of a water purification system. A mixture of water and pollutant flows into the vessel at a constant rate of x litres per minute. The proportion of pollutant in the mixture flowing into the vessel is q%. Pure water also flows into the vessel, at a rate of w litres per minute. In the vessel, the inflows are thoroughly mixed with the contents of the vessel. You may assume that this occurs instantaneously. The outflow from the vessel contains the same percentage of pollutant as the liquid in the vessel, and liquid flows out of the vessel at a rate of y litres per minute. (i) Given that at time t, in minutes, the volume of liquid in the vessel is V litres and the liquid in the vessel contains p% pollutant, show that dp dt qx-(w+x)p V [4] (ii) It is given that x=y=w=1000, and q = 40 and that at t = 0, V = 10000 and p=10. Use Euler's method with a step size of 1 minute to estimate p at t = 3. Explain whether you would expect this to be an underestimate or overestimate of the true value. [4] A vessel forms part of a water purification system. A mixture of water and pollutant flows into the vessel at a constant rate of x litres per minute. The proportion of pollutant in the mixture flowing into the vessel is q%. Pure water also flows into the vessel, at a rate of w litres per minute. In the vessel, the inflows are thoroughly mixed with the contents of the vessel. You may assume that this occurs instantaneously. The outflow from the vessel contains the same percentage of pollutant as the liquid in the vessel, and liquid flows out of the vessel at a rate of y litres per minute. (i) Given that at time t, in minutes, the volume of liquid in the vessel is V litres and the liquid in the vessel contains p% pollutant, show that dp dt qx-(w+x)p V [4] (ii) It is given that x=y=w=1000, and q = 40 and that at t = 0, V = 10000 and p=10. Use Euler's method with a step size of 1 minute to estimate p at t = 3. Explain whether you would expect this to be an underestimate or overestimate of the true value. [4]