Tanks A and B contain mixtures of water and a pollutant. Tank A has a 100 gallon capacity...

Tanks A and B contain mixtures of water and a pollutant. Tank A has a 100 gallon capacity and is full. Tank B is also full and has a 200 gallon capacity. Initially, tank A contains 40 pounds of pollutant and tank B contains pure water (no pollutant). At t = 0, pure water begins pouring into tank A at a rate of 10 gallons per minute. The mixture flows from tank A into tank B at a rate of 10 gallons per minute, and drains out of tank B at 10 gallons per minute. If xA and xB represent the number of pounds of pollutant in tank A and tank B, respectively, show that

where xA (0) = 40 and xB(0) = 0.

a) Use pplane6 and its zoom tools to estimate the maximum amount of pollutant in tank B and the time that it occurs.

b) Use pplane6 to estimate the time that it takes the pollutant in tank B to reach a level of 10 pounds. Note: This event occurs at two separate times, once as the pollutant level is rising in tank B, and a second time when the pollutant level is decreasing.