A tank contains 2960 L of pure water. Solution that contains 0.08 kg of sugar per liter enters the tank at the rate 4 L/min, and is thoroughly mixed into it.

Question

A tank contains 2960 L of pure water. Solution that contains 0.08 kg of sugar per liter enters the tank at the rate 4 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?

y(0)= ____ (kg)

(c) As t becomes large, what value is y(t) approaching ? In other words, calculate the following limit. limt→∞y(t)= ____ (kg)

Answer 1

You give the initial condition as 0 kg salt in the tank at time = 0 (pure water)

If t = time and S(t) is the amount of salt in the tank as a function of time, then....

The equation that I get is S(t) = 236.8(1 - e^(t/740) )

That means when time goes to infinity, the amount of salt in is 236.8 kg.