Atank initially contains 100 gallons of brine whose salt concentration is 3 lb/gal. fresh water is poured into the tank at a rate of 3 gal/min, and the well stirred mixture flows out of the tank at the rate of 5 gal/min.

a. find the initial-value problem that describes the amount of salt in the tank?

b. find the amount of salt in the tank after time t.

c. if you have access to a computer with graphing capabilities, sketch the graph of solution foind in (b).

2. initially, 5 pounds are dissolved in 20 gallons of water. a salt solution with a concentration of 2lb gallon is added to the tank at a rate of 3gal/min and the well stirred mixture is drained from the tank at same rate. how long should this mixture be added in order to raise the amount of salt in the tank to 25lb.

8. lake erie has a volume of roughly 100 cubic miles whose inflow and outflow rates are the same 40 cubics miles per year. suppose at the year t=0 a certain pollutant has a volume concentraion of .05% but thereafter the concentration of pollutant flowing drops to .01% assuming that the pollltant leaving the lake is well mixed with the lake water:

a. the initial value problem that describes the volume v of pollutant in the lake?

b. what is the volume v of pollutant in the lake at the time of t?

c. how long will it take to reduce the pollution concentration to .02% in volume?

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