A City's Water Reservoir Contains 7 Billion Cubic Meters (Bcm)

Short Answer

A city's water reservoir contains 7 billion cubic meters (bcm) of water. The purification system ensures that the concentration of pollutants remains constant at 0.6 kilograms per bcm, and sensors will trigger an alarm if the concentration of pollutants rises above 1 kilogram per bcm. Water flows in and out of the reservoir at the same rate of 0.25 bcm per day, and the concentration of pollutants in the inflow is 2 kilograms per bcm. At all times, the reservoir is well mixed.Set up a differential equation whose solution x(t) is the amount of pollutant in the reservoir at time t. Let t = 0 be the time when the purification system fails. What is x(0)?