A tank contains 100 liters of a fluid, in which 35 grams of Chemical X has been

Question

A tank contains 100 liters of a fluid, in which 35 grams of Chemical X has been dissolved. If fluid containing 4 grams of Chemical X per liter enters the tank at a rate of 3 liters per minute and the well-mixed solution exits the tank at 5 liters per minute, find the function A(t): the amount of Chemical X in the tank at a time t. Also, during this fill and drain process, what is the maximum amount of Chemical X in the tank? Please Answer all parts of this question for a rating. And show steps. Thank you. Mainly need to know how to find the maximum amount of chem x in tank.

Explanation / Answer

100dC/dt = 3*4 - 5C = 12 - 5C

20dC/(2.4 - C) = dt

20 ln((2.4-C0)/(2.4 - C) = t

C = 2.4 - (2.4- C0)e^(-t/20)

C0 = 35/100 = 0.35

C = 2.4 - 2.05e^(-t/20)

maximum amount of C = 2.4 gm/ltr

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