13. Pharmacokinetics. A simple model for the concentration C'(t) of a drug administered to a patient is based on the assumption that the rate of decrease of C(t) is negatively proportional to the amount present in the system, dC dt -kC, where k is a rate constant that depends on the drug and its value can be found experimentally. (a) Suppose that a dose administered at time t = 0 is rapidly distributed throughout the body, resulting in an initial concentration Co of the drug in the patient. Find C'(t), assuming the initial condition C(0) = Co. (b) Consider the case where doses of Co of the drug are given at equal time intervals T, that is, doses of Co are administered at times t = 0, T, 2T,.... Denote by Cn the concentration immediately after the nth dose. Find an expression for the concentration C₂ immediately after the second dose. (c) Find an expression for the concentration C₁ immediately after the nth dose. What is limn→∞ Cn?
13. Pharmacokinetics. A simple model for the concentration C'(t) of a drug administered to a patient is based on the assumption that the rate of decrease of C(t) is negatively proportional to the amount present in the system, dC dt -kC, where k is a rate constant that depends on the drug and its value can be found experimentally. (a) Suppose that a dose administered at time t = 0 is rapidly distributed throughout the body, resulting in an initial concentration Co of the drug in the patient. Find C'(t), assuming the initial condition C(0) = Co. (b) Consider the case where doses of Co of the drug are given at equal time intervals T, that is, doses of Co are administered at times t = 0, T, 2T,.... Denote by Cn the concentration immediately after the nth dose. Find an expression for the concentration C₂ immediately after the second dose. (c) Find an expression for the concentration C₁ immediately after the nth dose. What is limn→∞ Cn?
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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Transcribed Image Text:13. Pharmacokinetics. A simple model for the concentration C'(t) of a drug administered to a
patient is based on the assumption that the rate of decrease of C(t) is negatively proportional to
the amount present in the system,
dC
dt
-kC,
where k is a rate constant that depends on the drug and its value can be found experimentally.
(a) Suppose that a dose administered at time t = 0 is rapidly distributed throughout the body,
resulting in an initial concentration Co of the drug in the patient. Find C'(t), assuming the initial
condition C(0) = Co.
(b) Consider the case where doses of Co of the drug are given at equal time intervals T, that is,
doses of Co are administered at times t = 0, T, 2T,.... Denote by Cn the concentration
immediately after the nth dose. Find an expression for the concentration C₂ immediately after the
second dose.
(c) Find an expression for the concentration C₁ immediately after the nth dose. What is
limn→∞ Cn?
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