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?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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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