A tank contains $1060$ L of pure water. A solution that contains $0.09$ kg of sugar per liter enters the tank at the rate $7$ L/min. The solution is mixed and drains from the tank at the same rate.

(a) How much sugar is in the tank at the beginning?
$y(0) =$ (include units)

(b) With $S$ representing the amount of sugar (in kg) at time t (in minutes) write a differential equation which models this situation.
$S' = f(t,S) =$ .
Note: Make sure you use a capital S, (and don't use S(t), it confuses the computer). Don't enter units for this function.

(c) Find the amount of sugar (in kg) after t minutes.
$S(t) =$ (function of t)

(d) Find the amount of the sugar after 30 minutes.
$S(30)=$ (include )