Let x(t) represent the amount of salt (grams) in a 15 liter tank after t minutes

Question

Let x(t) represent the amount of salt (grams) in a 15 liter tank after t minutes. A solution whose salt concentration is 13 g/L flows into the tank at a rate of 10 L/min and the tank is continuously stirred while being drained at a rate of 10 L/min. The differential equation in terms of x(t) would then be dx/dt + 0.67 x = 130. Let C(t) represent the concentration of salt in the tank after t minutes. Convert the differential equation to be in terms of C(t) and then isolate dC/dt. dC/dt = 8.6666666666667- 0.66666666666667.C

Explanation / Answer

We have dx/dt + 0.67x = 130

We also know that C(t) = x/15

On plugging this value in the differential equation:

15dC/dt + 15(0.67C) = 130

15dC/dt + 10.05C = 130

Diving by 15 on both sides:

dC/dt = 8.6666666666 - 0.66666666666C

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