Problem 4.11. The Lake Cachuma reservoir system is actually more complex than we let on earlier. Really, runâ€”off water ï¬‚ows mostly into the Gibraltar Reservoir, water from Gibraltar Reservoir ï¬‚ows into Lake Cachuma, and we take water from Lake Cachuma for drinking water. Instead of tracking nitrates, we will track mercury in this problem. a. Suppose water ï¬‚ows into Gibraltar at a rate of 7â€˜9 with mercury concentration 0; water ï¬‚ows from Gibraltar into Cachuma at a rate of re; and we drain Cachuma at a rate of rd. Write a system of differential equations which model the total masses Ag and Ac of mercury in each lake. b. Suppose Cachuma and Gibraltar each have volumes of 10 trillion L, and the three ï¬‚ow rates are all equal to 1 trillion L per month: r9 2 rc 2 rd 2 1. Currently neither lake has any mercury at all, but authorities want to plan for the possibility of a rockslide at the Sunbird Quicksilver Mine, which could deposit up to 10kg of mercury directly into Gibraltar. If this happens, what would be the maximum concentration of mercury that occurs in Cachuma?
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