1. Tired of life in Springfield, Mr. Burns has purchased "El Nuevo Plateado" mining camp in Sierra Nevada, along with the nearby "El Arsénico" well. Eager to conclude the deal, Mr. Burns exclaimed to the seller, Sr. Delgado: "El Artesiano - mmm, que agua tan pura!" and muttered "so cheap!" under his breath. Although he is primarily interested in enriching himself by selling the silver mined in the camp, Mr. Burns has graciously agreed to arrange for the camp's provisions in exchange for the wage reductions to cover his additional costs. El Nuevo Plateado has a 4000 gal reservoir of potable water for drinking and cooking. The camp consumes 600 gal per day and replenishes its water supply by pumping 400 gal per day from the well. Unfortunately, due to the mining activities, the groundwater has been contaminated with arsenic at 50?g/L, which is equivalent to 50 parts per billion (ppb). Of course, Mr. Burns does not care, but others might! 1gal=3.785 L,1?g=10000001? g=10?9 kg,1 billion =109 (a) On February 1, the reservoir was emptied, cleaned and filled with pure water delivered from pristine Lake Dejou 100 miles away ("so far!" sighed Mr. Burns). Assuming that the liquid in the reservoir is continuously mixed, develop a mathematical model for the concentration of arsenic in the reservoir as a function of time. Your model should specify a consistent system of units, describe the variables and include differential equations and initial conditions for the total volume of water and the amount of arsenic. (b) Without any adjustments to the water usage, how long would the current potable water supply in El Nuevo Plateado last? (c) The next water delivery is scheduled in two weeks. The U.S. Environmental Protection Agency (EPA) currently recommends that in order to avoid adverse health effects, the arsenic concentration in the drinking water must not exceed the maximum contaminant level (MCL) of 10?g/L, or 10ppb. Will the camp's potable water supply be in compliance with the EPA rule through the scheduled water delivery date? If not, when will the arsenic level exceed the EPA-recommended limit?