pump water from lake B at a rate a cubic meters per day to b

pump water from lake B, at a rate a (cubic meters per day) to be determined, filter out the dioxin, and pump the filtered water back into lake A. NEED HELP WITH DERIVING EQUATIONS AND BACKGROUND INFORMATION

Two small lakes in South Alabama have been contaminated by the rather nasty carcino- gen dioxin released from a local paper mill The EPA has ordered the mill owners to clean up the lakes within one year, and they in turn have hired you as a consultant to model the clean up process and in particular to recommend an effective strategy for doing this in the allotted time. Filter Pump rate a Lake B Lake A Stream 3 Stream 1 Stream 2

Solution

The first proposal implies increasing the conc of pond 1 by .2 c₀ (100-80)/100 =.2

The eqn is dC/dt =0.2C

soln C = Aexp(.2t), t in days

means the conc of toxin A will increase exponential with time.

So in 1 day, for the present level of dioxin ( not found in the statement of problem), the conc increases to A(1+e)

B) want to reduce the flow rate to addnl 13000 from 30,000 so the constant A becomes 43/30 of the previous

43/30 *(1+exp(.2t) ) is the present increased amount per day.

C) want a new rate constant x instead of .2 so that 43/30(!+exp(xt)) = exp( 1+exp(.2t))

t=365 days, find x

(Pl check with Bing) Initial conc of pollutant not known. This formulation is for the same level of initial conc.

Best