A $100-$gal$-$capaeity electrolytic cell is charged with a solution containing $10$ g moles$/$ltr

of electrolyte. The level in the cell is kept constant by a float actuated valve; thus,

evaporation losses are replenished with stream of fresh water. When the cell operates,

the electrolyte is decomposed at the rate of $0\mathrm{.}5$ g mole $/$litre$/$hr$.4$ hr after the current is

turned on$,$ a corrosion leak develops in the lower longitudinal seam. This leak gets

progressively worse, the rate of loss in litres$/$hr being empirically described by the

relation v$=10$t$+5$t$2$

$-120.$ Set up an equation$($s$)$ which will relate concentration of

electrolyte $($g moles$/$litre$)$ in the tank as a function of time $($t in hr$)$ since the current Was

first turned on; i$.$e$.,$ the leak started at t$=4$