Question 2: 20 Marks A tank with a capacity of 3000 litres contains a solution of Saline (salt water) that is produced t

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Question 2 20 Marks A Tank With A Capacity Of 3000 Litres Contains A Solution Of Saline Salt Water That Is Produced T 1 (141.18 KiB) Viewed 70 times

Question 2: 20 Marks A tank with a capacity of 3000 litres contains a solution of Saline (salt water) that is produced to supply Ukrainian Hospitals during the war. The tank is always kept full. Initially the tank contains 15 kg of salt dissolved in the water. Water is pumped into the tank at a constant rate of 250 litres per minute, with 0.5 kg of salt dissolved in each litre of water. The contents of the tank are stirred continuously, and the resulting solution is pumped out at a rate of 250 litres per minite. Let S(t) denote the amount of salt (in kilograms) in the tank after t minutes and let C(t) denote the concentration of salt (in kilograms per litre) in the tank after t minutes. (2.1) Write down the differential equation for S(t) and C(t). (2.2) Draw the phase lines of the differential equations for the systems for S and C, and draw rough sketches of the values of S and C as functions of time, if their initial values are as specified above. (2.3) What will happen to S and C when t → ∞?