Question

Mathematical modeling using derivatives Example 9 A 1000 L holding tank that catches runoff from some chemical process initially has 800 L of water with 2 g of pollution dissolved in it. Polluted water flows into the tank at a rate of 3 L/hr and contains 5 g/L of pollution in it. A well mixed solution leaves the tank at 3 L/hr as well. When the amount of pollution in the holding tank reaches 500 g the inflow of polluted water is cut off and fresh water will enter the tank at a decreased rate of 2 L/hr while the outflow is increased to 4 L/hr. Determine the amount of pollution in the tank at any time t. Solution Continue in class

Answer 1

An 3 L /h (o): 오 fors- 206 - df 906 ay = 12000-38 - Is-3 dt 20 U 12000-3 3 | 12,000-3p| = 200 e-3/gcot -) 3B -,:@ whoe. Cl.c 12,000-C

S: 399 8 875 300 the ond Poca rabe, So Colds en a t dt 87 6. 950-26 d b 870.50 2t dt +C 970,950 2t

1(702 P(35, 475) -560 5000.9502x 35, 425) 30 0 9Asefge, the armcent of pollutant qn the lamと 4000-3118 c %eo o.625.(970.956-)5 7200é 35.425