A tank contains Lim _ t rightarrow infinity y(t) = (kg) y(t) approaching ? In ot

Question

A tank contains Lim _ t rightarrow infinity y(t) = (kg) y(t) approaching ? In other words, calculate the following limit. y(t)= (kg) (c) As t becomes large, what value is y(0)= (kg) (b) Find the amount of sugar after t minutes. 9 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate. (a) How much sugar is in the tank at the begining?0.04kg of sugar per liter enters the tank at the rate1840L of pure water. Solution that contains n the resulting solution?

Explanation / Answer

If there's .01kg/liter entering, at 3L/min,that's .03kg/minute. That's important :). dS/dt = .03 - D (The rate at which the sugar level (S) changes per minute (t) = the rate at which sugar enters minus the rate at which it leaves) D= kS ( The drainage rate is proportional to the amount of sugar) So, substituting: dS/dt=.03 - kS Now, get dt alone: dS =(.03 -kS)dt dS/(.03-kS)=dt 1/(.03-kS) * dX = dt Now: INTEGRATE :) -ln | .03 -kS | + C1 = t + C2 (Each side has a different arbitrary C) subtracting the arbitrary C1 from both sides, we get a new arbitrary C on the right: -ln|.03-kS|=t+C3 ln|.03-kS|=-t-C4

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