A tank contains $1400$ L of pure water. Solution that contains $0.06$ kg of sugar per liter enters the tank at the rate $3$ 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)

(b) Find the amount of sugar after t minutes.
$y(t) =$ (kg)

(c) As t becomes large, what value is $y(t)$ approaching ? In other words, calculate the following limit. $\displaystyle \lim_{t \to \infty} y(t) =$ (kg)