Atank contains 1600 l of pure water. solution that contains 0.04 kg of sugar per liter enters the tank at the rate 2 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?
(b) find the amount of sugar after t minutes.
(c) as t becomes large, what value is y(t) approaching ? in other words, calculate the following limit y(t) as t approcahes infinity.

Let S(t) denote the amount of sugar in the tank at time t. Sugar flows in at a rate of

(0.04 kg/L) * (2 L/min) = 0.08 kg/min = 8/100 kg/min

and flows out at a rate of

(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min

Then the net flow rate is governed by the differential equation

Solve for S(t):

The left side is the derivative of a product:

Integrate both sides:

There's no sugar in the water at the start, so (a) S(0) = 0, which gives

and so (b) the amount of sugar in the tank at time t is

As , the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.

  about 5.6 days

step-by-step explanation:

we can fill the given information into the decay equation and solve for the value of t at which half the sample remains.

the half-life is about 5.6 days.

8121 because

130,000 divided by 16 is 8121