A lake contains 60 million cubic meters (2MCM) of water. Each year a nearby plant adds 8.5 grams of mercury to the lake. Each year 2MCM of lake water are replaced with mercury-free water.
1. What is the differential equation that governs the amount of mercury in the lake?
2. According to your differential equation how much mercury will be present in the lake in the long run?
3. Supposed that in 1940 the power plant began contributing 8.5 grams pf mercury per year into the lake. In 2000 the plant reduced its pollution to 2 grams annually. In what year the will the mercury level fall below 120 grams?
The solution is 4 pages long in which a detailed procedure of converting the question to a differential equation and then solving it is described.