An antibiotic is administered intravenouslyinto the bloodstream at a constant rate r. As the drug flowsthrough the patient’s system and acts on the infection that is present,it is removed from the bloodstream at a rate proportional tothe amount in the bloodstream at that time. Since the amount ofblood in the patient is constant, this means that the concentrationy = y(t) of the antibiotic in the bloodstream can be modeled bythe differential equation dy/dt = r - ky, k > 0 and constant. If y(0) = y0, find the concentration y(t) at any time t.
An antibiotic is administered intravenouslyinto the bloodstream at a constant rate r. As the drug flowsthrough the patient’s system and acts on the infection that is present,it is removed from the bloodstream at a rate proportional tothe amount in the bloodstream at that time. Since the amount ofblood in the patient is constant, this means that the concentrationy = y(t) of the antibiotic in the bloodstream can be modeled bythe differential equation dy/dt = r - ky, k > 0 and constant. If y(0) = y0, find the concentration y(t) at any time t.
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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An antibiotic is administered intravenously
into the bloodstream at a constant rate r. As the drug flows
through the patient’s system and acts on the infection that is present,
it is removed from the bloodstream at a rate proportional to
the amount in the bloodstream at that time. Since the amount of
blood in the patient is constant, this means that the concentration
y = y(t) of the antibiotic in the bloodstream can be modeled by
the differential equation
dy/dt = r - ky, k > 0 and constant. If y(0) = y0, find the concentration y(t) at any time t.
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