$(8$ points$)$ Consider a drinking water tower with a volume of $2,500m^3$ that is used to store treated drinking water. The drinking water utility plans to install a chlorine meter and must take the tower out of service for several hours. During this time, no water flows into or out of the tank. At the time the tower was taken out of service, the concentration of chlorine in the water tower was $3\mathrm{.}5m\frac{g}{L}.$

a$.$ If the chlorine decays with a rate constant of $1\mathrm{.}0d^{-1},$ what is the chlorine concentration when the tank is put back in service $6$ hours later?

b$.$ What mass of chlorine $($in kg $)$ must be added to the tank to raise the level back to $3\mathrm{.}5m\frac{g}{L}?$ For this problem, assume the tank is well$-$mixed.