(Solved): (b) A 10kL tank of water provides water for a small village. Water is drunk from the tank at a rate ...

(b) A $10kL$ tank of water provides water for a small village. Water is drunk from the tank at a rate of $1000\mathrm{L}$ per day, and the water is replenished at the same rate. Unfortunately, the filter/purifier for the intake water is malfunctioning. Consequentially the water that is replenishing the tank is contaminated; it contains $0.00125\mathrm{mg}/\mathrm{L}$ of heavy metals. Suppose that when the contamination was discovered the tank was $3/4$ full and contained $a_{s}mg$ of heavy metals. (i) Find a formula, $A(t)$, for the amount of heavy metals in the tank at time $t$. Hint: make sure your units are consistent for all quantities. We suggest $\mathrm{mg}/\mathrm{kL}$