NOTE: This problem was used as a midterm problem in the past:

You are working for an engineering firm when your supervisor asks you to consider the following

scenario. Please write your answer to this question as if you were documenting your analysis for

your supervisor $($Hint: The format of your problem sets is useful$).$

A harmful algal bloom of cylindrospermopsin has been detected in a shallow well$-$mixed lake. The

lake maintains a constant volume of $10,000m^3.$ Currently the cylindrospermopsin concentration in

the lake is $500\frac{g}{L}.$ The EPA recommends people should stay away from water where

concentrations exceed $15\frac{g}{L}.$ Cylindrospermopsin has also been detected in the stream that flows

out of the lake. However, it has not been detected in the stream that flows into the lake, which has a

flow rate of $1,000\frac{m^3}{d}ay.$ The production of cylindrospermopsin in the lake is a first order

process, with $k=\frac{0\mathrm{.}5}{d}ay.$ The lake is a popular place for swimming especially on Homecoming

weekend. Community members have asked environmental managers to consider applying a clay

treatment to remove the algae from the lake so that it will be ready for swimming by Homecoming

weekend, which will happen $7$ days later. Assuming the clay treatment will remove

cylindrospermopsin at $2,100\frac{g}{d}ay,$ will the lake be safe for swimming by Homecoming weekend

if this treatment is applied immediately? Show all of your work to make a recommendation to your

supervisor. Clearly state how you think the community should address this problem.