A 5000-gal aquarium is maintained with a pumping system that passes 100 gal of water per minute through the tank. To treat a certain fish malady, a soluble an- tibiotic is introduced into the inflow system. Assume that the inflow concentration of medicine is 10te^−(t/50) mg/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) For the antibiotic to be effective, its concentration must exceed 100 mg/gal for a minimum of 60 min. Was the dosing effective?
A 5000-gal aquarium is maintained with a pumping system that passes 100 gal of water per minute through the tank. To treat a certain fish malady, a soluble an- tibiotic is introduced into the inflow system. Assume that the inflow concentration of medicine is 10te^−(t/50) mg/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) For the antibiotic to be effective, its concentration must exceed 100 mg/gal for a minimum of 60 min. Was the dosing effective?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A 5000-gal aquarium is maintained with a pumping system that passes 100 gal of water per minute through the tank. To treat a certain fish malady, a soluble an- tibiotic is introduced into the inflow system. Assume that the inflow concentration of medicine is 10te^−(t/50) mg/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) For the antibiotic to be effective, its concentration must exceed 100 mg/gal for a minimum of 60 min. Was the dosing effective?
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