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

A certain type of bacteria is known to grow at the rate proportional to the amount that is present. If you start with 2 grams of the bacteria and in two hours there are 2.1 grams, how much you will have after 5 hours ?

5. Suppose that sodium pentobarbital is used to anesthetize a dog. The dog is anesthetized when its bloodstream contains at least 45 milligrams (mg) of sodium pentobarbitol per kilogram of the dog's body weight. Suppose also that sodium pentobarbitol is eliminated from the dog's bloodstream at a rate which is proportional to the amount of sodium pentobarbitol in the bloodstream and that after 5 hours half of the initially prescribed sodium pentobarbitol is elliminated from the bloodstream. Set up and solve an initial value differential equation. What single dose should be administered in order to anesthetize a 50-kg dog for 1 hr?