A shallow reservoir has a one$-$square$-$kilometer water surface and an average water depth of $2$ meters. Initially it is filled with fresh water, but at time $t=0$ water contaminated with a liquid pollutant begins flowing into the reservoir at the rate of $200$ thousand cubic meters per month. The well$-$mixed water in the reservoir flows out at the same rate. Your first task is to find the amount $x(t)$ of pollutant $($in millions of liters$)$ in the reservoir after $t$ months. The incoming water has a pollutant concentration of $c(t)=30$ liters per cubic meter $(\frac{L}{m^3}).$ Verify that the graph of $x(t)$ resembles the steadily rising curve shown here, which approaches asymptotically the graph of the equilibrium solution $x(t)-=60$ that corresponds to the reservoir's long$-$term pollutant content. How long does it take the pollutant content in the reservoir to reach $15$ million liters?