A 20,000 litre aquarium is maintained with a pumping system that passes 350 litr

Question

A 20,000 litre aquarium is maintained with a pumping system that passes 350 litres 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 2.5te-t/50 mg/litre, where t is measured in minutes. The well-stirred mixture flows out of the aquarium at the same rate. Solve for the amount of medicine in the tank as a function of time. What is the maximum concentration of medicine achieved by this dosing and when does it occur? For the antibiotic to be effective, its concentration must exceed 25 mg/litre for a minimum of 60 min. Was the dosing effective?

Explanation / Answer

after time t vol=20000+350t a)weight of medicine=2.5t*e^-t/50 *350t=875t^2*e^-t/50 mg b)conc=(875t^2*e^-t/50 )/(20000+350t) mg/lit dc/dt=0 at max we get it at t=72.1 min max conc=23.77 mg/lit at t=72.1 min c)at t=60min c=23.14 mg/lit so dosingwas not effective to go over 25 mg/lit in 60 min

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