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Drug concentration An antibiotic is administered
Chapter 7, Problem 32E(choose chapter or problem)
Problem 32E
Drug concentration 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
= r - ky, k
and constant.
dt
If y (0) = y0, find the concentration y(t) at any time t.
Assume that y0 < (r/k) and find limy
Questions & Answers
QUESTION:
Problem 32E
Drug concentration 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
= r - ky, k
and constant.
dt
If y (0) = y0, find the concentration y(t) at any time t.
Assume that y0 < (r/k) and find limy
Solution:
Step 1 of 6:
a)In this problem, we need find the concentration at any time
.