Problem $12.$ A tank initially contains $10$ liters of water and $5$ grams of salt. Salt water containing $\backslash (3+$e$^\{-2$ t$\}\backslash )$ grams of salt per liter is pumped into the tank at a rate of $2$ liters per minute. The solution of salt water is instantaneously, perfectly mixed and then pumped out at a rate of $2$ liters per minute.

Determine when, to three decimal places, the concentration of the salt leaving the tank is within $\backslash (0\mathrm{.}01\backslash$mathrm$\{$grams$\}/\backslash$mathrm$\{$liter$\}\backslash )$ of the salt entering the tank.