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4.(12 pts) A 20,000 liter tank is initially half full with 10,000 liters of 2% nitric...

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4.(12 pts) A 20,000 liter tank is initially half full with10,000 liters of 2% nitric acid. A solution of 5% nitric acid ispumped in at a rate of 30 liters per minute and the well mixedmixture is pumped out at the same rate of 30 liters per minute.

(a)(8 pts) Set up (But Don’t Solve) an IVP whose solution givesthe amount of x(t) of pure nitric acid (in liters) in the tank attime t

(b)(4 pts) Use a quick qualitative analysis of the IVP you foundin part (a) to predict how much pure nitric acid will be in thetank as t?infinity(Show a phase line or direction field to predictwhat happens as t?infinity

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