A tank contains 200 liters of fluid in which 30 grams of salt is 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 slower rate of 3 L/min. Write a differential equation that models the amount of salt in the tank at any time.

Salt flows in at a rate of

(2 g/L) * (4 L/min) = 8 g/min

and out at a rate of

(B/(200 + t) g/L) * (3 L/min) = 3B/(200 + t) g/min

where B is the amount of salt in the tank at time t.

Then the net rate at which B changes is governed by the ODE,

Multipy both sides by :

Integrate both sides:

The tank starts with 30 g of salt, so B(0) = 30, which gives

you answer is a

step-by-step explanation:

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step-by-step explanation

2r= 2300

r =1150