Jenny

Mathematics

10 April, 15:49

Example 2.3.6. Consider a fish tank that initially contains 150 liters of water with 20 grams of salt (pollutant) dissolved in it. The salt concentration in the tank needs to be increased from 20/150 grams per liter to 1 gram per liter to accommodate a new species of fish. Water containing 3 grams of salt per liter is allowed to run into the tank at a rate of 2 liters per minute. The thoroughly stirred mixture in the tank is also allowed to drain out at the same rate of 2 liters per minute. Find a differential equation for the amount of salt x (t) in the tank at time t. Use the initial condition x (0) = 20 to find the time it will take to increase the salt concentration in the tank to 1 gram per liter.