A 5000 gallon aquarium is maintained with a pumping system that circulates 100 gallons of water per minute through the tank. To treat a certain fish malady, a soluble antibiotic is introduced into the inflow system. Assume that the inflow concentration of medicine is 10te-t/50 oz/gal, where t is measured in minutes. The well-stirred mixture flows out of the aquarium at the same rate.
a) Solve for the amount of medicine in the tank as a function of time.
b) What is the maximum concentration of medicine achieved by this dosing and when does it occur?
c) To be effective, the antibiotic concentration must exceed 100 oz/gal for a minimum of 60 minutes. Was the dosing effective?
Exponential functions are used to calculate flow rates. The solution is detailed and well presented.