A lake represented as a CMFR

Consider the concentration of lead in a lake, using a simplified model. The lake has a

river flowing into it and another following out of it$,$ and the water level in the lake is

constant. The major sources of lead in the lake are direct deposit from the atmosphere

and surface runoff carried into the lake with the river. The major removal process is river

outflow. Leaded gas was widely used for about $35$ years $($roughly $1950$ to $1985),$ leading

to a high influx of lead into the lake during those years. Use a CMFR representation of

the lake to calculate the growth and decay of lead concentration in the lake.

a$.$ Derive an analytical expression that describes the lead concentration in the lake

water as a function of time beginning in $1950.$

b$.$ Plot the lead concentration versus time $(1950-2050)$ in the lake water

c$.$ Assume the drinking water limit for lead is $15ppb.$ During which years, if any is

the water unsuitable for drinking because of the lead concentration?

Data

Lake Volume $=5{10}^9{m}^3$

River inflow $=$ river outflow $=3{10}^8{m}^{3}y{r}^{-1}$

$Pb$ in lake water, $1950=3ppb$

$Pb$ in influent to river water, $1950-1985=30ppb$

$Pb$ in influent to river water, $1985-2050=5ppb$

$Pb$ deposition from the atmosphere

$1950-1985=3000kgy{r}^{-1}$

$1985-2050=300kgy{r}^{-1}$

Please solve and show all steps, will give thumbs up if correct!