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5. (Mixing Problem) A very large tank is initially filled with 100 gallons of water containing...

5. (Mixing Problem) A very large tank is initially filled with 100 gallons of water containing 5 pounds of salt. Beginning at time t = 0, a brine solution with a concentration of 1 pound of salt per gallon flows into the top of the tank at 3 gallons per second, the mixture is stirred, and the mixture flows out of the bottom of the tank at 2 gallons per second. (a) Letting w = pounds of salt in the tank at time t seconds, derive a differential equation using the principle dw dt = rate in − rate out. (b) Find a formula for w in terms of t by solving the differential equation in Part (a) after first expressing it in the form P(t, w) dt + Q(t, w) dw =0

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Colby Messinger answered 2 years ago
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