A tank of volume 400 L initially contains 20 g of salt. A salt brine of concentration 3 g/L is pumped into the tank at the rate of 10 L/min, and the perfectly stirred mixture is pumped out at the same flow rate. Let y = y(t) be the amount of salt in the tank at t minutes after the process begins. (a) Set up the IVP (= Initial Value Problem = DE + Initial Condition). (b) Solve the IVP to find the formula for y(t). (c) How much salt is in the tank after 60 minutes? (d) What happens in the long run? Use the formula you found in #2 to explain quantitatively.
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We need to set up the differential equation that describes the rate of change of salt in the tank. We know that salt is being pumped in at a rate of 3 g/L and the volume of the tank is changing at a rate of 10 L/min. Therefore, the rate of change of salt in the Show more…
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Madhur L.
(25 pts) A 500-liter tank initially contains 10 grams of salt dissolved in 200 liters of water. Starting at time 0, water that contains 1/4 gram of salt per liter is poured into the tank at a rate of 4 liters per minute. And the mixture is drained from the tank at a rate of 2 liters per minute. (a) Find a differential equation for the quantity Q(t) of the tank at time t prior to the time when the tank overflows. Find the concentration C(t) in grams per liter of salt in the tank at any such time.
A tank contains 200 liters of fluid in which 30 grams of salt are dissolved. Brine containing 2 grams of salt per liter is then pumped into the tank at a rate of 4 L/min. The well-mixed solution is pumped out at a faster rate of 5 L/min. Set up an initial value problem (a differential equation with an initial condition) to find the amount of salt Q(t) in the tank at any time t. (Do not solve the equation).
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