Question

(1 point) A tank contains 1600L of pure water. Solution that contains 0.08 kg of sugar per liter enters the tank at the rate 6 Umin, 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? (kg) (b) Find the amount of sugar after t minutes kg) c) As t becomes large, what value is y) approaching ? In other words, caliculate the following limi im yt) kg)

Answer 1

is the equation

6y(t) y'(t)0.08 x 6 - Dy(t) 0.48- 1600 1600

So is the equation

y'(t)y=0.48 1600

At the beginning we have

y(0)= 0

In the limit we have (as the amount of sugar will have stabilized)

y'(t)0

So that

6y(t) 0.48 x 1600 0.48 y(t) 1600

That is, in the limit we have

lim y(t) 128

$\blacksquare$

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