1 4 A wellcirculated pond contains 1 million L of water that

1. 4. A well-circulated pond contains 1 million L of water that contains a pollutant ata concentration of 0.01 kg/L. Pure water enters from a stream at 100 L/h. Waterevaporates from the pond (leaving the pollutant behind) at 50 L/h. How manydays will it take for the concentration of pollutant to drop to 0.001 kg/L?

2. A 100-gal tank is initially full of water containing 10 lb of salt in solution. Thetank will overow whenever additional water is added. A pump attached to asensor pumps fresh water into the tank at a rate proportional to the concentrationof salt in the tank. The constant of proportionality is 10 (gal) 2 /lb · min. Find theamount and concentration of salt in the tank as functions of t .

3. A 600-gal tank initially contains 200 gal of brine (salt water) with 25 lb of salt.Brine containing 2 lb of salt per gallon enters the tank at the rate of 13 gal/s.The mixed brine in the tank ows out at the rate of 8 gal/s. How much salt isthere in each tank as a function of time?

Solution

Solution :(2)

At 0 time, 10 pounds of salt, 100 gal water, rate starts at 1000 gal/min.
If rate remained constant, then after 0.1 minute, 5 pounds salt, 100 gal water
When 9 pounds of salt, 100 gal water, rate is 900 gal/min
When 8 pounds of salt, 100 gal water, rate is 800 gal/min
s = 10e^(-kt)
ln(s/10) = -kt
ln(0.9) = -0.105360516 = -kt
t = 0.105360516/k minute for 9 pounds
t = 0.223143551/k minute for 8 pounds
t = 0.693147181/k minutes for 5 pounds