$(1$ point$)$ A tank, containing $400$ liters of liquid, has a brine solution entering at a constant rate of $4$ liters per minute. The well$-$stirred solution leaves the tank at the same rate. The concentration within the tank is monitored and found to be

$c(t)=\frac{e^{\frac{-t}{400}}}{40}k\frac{g}{L}$

a$.$ Determine the amount of salt initially present within the tank.

Initial amount of salt $=$ kg

b$.$ Determine the inflow concentration $c_{in}(t),$ where $c_{in}(t)$ denotes the concentration of salt in the brine solution flowing into the tank.

$c_{in}(t)=$

$k\frac{g}{L}$