Suppose a brine containing $0\mathrm{.}2kgof$ salt per liter runs into a tank initially filled with $500Lof$ water containing $2kgof$ salt. The brine enters the tank $at$ a rate $of$

$5\frac{L}{m}in.$ The mixture, kept uniform $by$ stirring, $is$ flowing out $at$ the rate $of5\frac{L}{m}in.$ Complete parts $(a)$ and $(b).$

$(a)$ Find the concentration, $in$ kilograms per liter, $of$ salt $in$ the tank after $5$ min $.[Hint$: Let A denote the number $of$ kilograms $of$ salt $in$ the tank $at$ minutes after the process begins and use the fact that

rate $of$ increase $inA=$ rate $of$ input $-$ rate $of$ exit.$]$

The concentration $of$ salt $in$ the tank after $5$ min will $be0\mathrm{.}0136k\frac{g}{L}.$

$(Roundto$ four decimal places $as$ needed.$)$

$(b)$ After $5$ min $,$ a leak develops $in$ the tank and $an$ additional liter per minute $of$ mixture flows out $of$ the tank. What will $be$ the concentration, $in$ kilograms

per liter, $of$ salt $in$ the tank $20$ min after the leak develops?

The concentration $of$ salt $in$ the tank $20$ min after the leak develops will $bek\frac{g}{L}.$

$(Roundto$ four decimal places $as$ needed.$)$