Only one Big Picture sketch is required per problem, clearly label which parameters apply for specific

parts of the problem.

Lake Roland has two streams entering the lake: the Jones Falls and Towson Run. The annual

average lake volume is $2*{10}^5{m}^3.$ The annual average inflows from the Jones Falls and Towson

Run are $0\mathrm{.}6*{10}^5\frac{m^3}{y}r$ and $0\mathrm{.}4*{10}^5\frac{m^3}{y}r,$ respectively. The annual overflow from the dam spillway

is $0\mathrm{.}9*{10}^5\frac{m^3}{y}r.$ The average phosphorus concentrations in the Jones Falls and Towson Run are $1\mathrm{.}0$

$\frac{g}{L}$ and $2\mathrm{.}0\frac{g}{L},$ respectively. The average phosphorus concentration in the lake outflow is $1\mathrm{.}5$

$\frac{g}{L}.$ Treat each subsequent part as different scenarios.

a$)$ What is the rate of change in the lake volume in $\frac{m^3}{y}r?$

b$)$ Assuming that the phosphorus is conservative and the lake volume is at steady$-$state $($as first cut

approximation$),$ what is the rate of change of the lake concentration in $\frac{g}{L}\frac{?}{yr}?$

c$)$ If the lake volume and concentration are at steady$-$state and we assume that phosphorus is not

conservative, what is the rate of production or consumption in the system in $\frac{g}{L}\frac{?}{yr}?$ Assume a

first order reaction. How would you interpret this result?