Consider a well$-$mixed lake with a mean depth of $1\mathrm{.}25$ meters and a surface area of $800000$ square meters. The lake is situated in an agricultural region where pesticide usage is widespread. The lake receives a pesticide flux from the atmosphere equal to $0\mathrm{.}25\frac{g}{m^2}.$day. The influent stream $($streamflow $=60000\frac{m^3}{?}$ day$)$ has a pesticide concentration of $4m\frac{g}{L}.$ The pesticide is present in the lake in two states $($adsorbed and dissolved$)$ with a partition coefficient of $0\mathrm{.}035\frac{m^3}{g}.$ It is known that the dissolved pesticide decays biologically with a rate constant of $0\mathrm{.}12\frac{1}{?}$ day while the suspended solids in the lake $($SS concentration in the lake is $75m\frac{g}{L})$ protect the adsorbed pesticide from decaying. The suspended solids settle with a velocity of $0\mathrm{.}44\frac{m}{?}$ day and the pesticide volatilizes with $0\mathrm{.}16\frac{m}{?}$ day.

a$)$ Find the steady state total, dissolved and particulate pesticide concentrations in the lake

b$)$ Find how much pesticide biodegrades, settles, volatilizes and is flushed out.

c$)$ Find the assimilation percentage of the lake

d$)$ Find the $99\%$ response time of the lake.