A$.$ SO$-$gallon Barrel is filled completely with pure water. Salt water with a concentration of $0\mathrm{.}3$ pounds$/$gallon is then pumped time t $($in minutes$)$ is given by $Q(t)=15(1-e^{-4t})$ where $k>0.$

$($a$)$ Find tet there are $12\mathrm{.}5$ pounds of sult in the barrel after $30$ minutes. Round your answer to $4$ declmal places. k $*$

$($b$)$ What hapfens lo the amount of salt in the barrel as $t?$

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