3.7. A chemical with a half-life of 1 day is produced at a constant rate of 10 μM h-¹. Suppose its concentration is denoted C(t) and let C(0) = Co. (a) Use a differential equation to describe the dynamics of this process. (b) If an inhibitor is applied at t = 0, so that the chemical is no longer produced, find the solution to C(t) and use that solution to show that C → 0 as t→∞. (c) Suppose that starting from C(0) = Co, we instead apply a drug that suppresses the turnover of this chemical completely, but leaves the original production rate intact. Show that the chemical will accumulate at a linear rate C(t) = Co+kt. What is the accumulation rate (value of the constant k)?
3.7. A chemical with a half-life of 1 day is produced at a constant rate of 10 μM h-¹. Suppose its concentration is denoted C(t) and let C(0) = Co. (a) Use a differential equation to describe the dynamics of this process. (b) If an inhibitor is applied at t = 0, so that the chemical is no longer produced, find the solution to C(t) and use that solution to show that C → 0 as t→∞. (c) Suppose that starting from C(0) = Co, we instead apply a drug that suppresses the turnover of this chemical completely, but leaves the original production rate intact. Show that the chemical will accumulate at a linear rate C(t) = Co+kt. What is the accumulation rate (value of the constant k)?
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:3.7. A chemical with a half-life of 1 day is produced at a constant rate of 10 µM h-¹.
Suppose its concentration is denoted C(t) and let C(0) = Co.
(a) Use a differential equation to describe the dynamics of this process.
(b) If an inhibitor is applied at t = 0, so that the chemical is no longer produced,
find the solution to C(t) and use that solution to show that C → 0 as t→∞0.
(c) Suppose that starting from C(0) = Co, we instead apply a drug that suppresses
the turnover of this chemical completely, but leaves the original production rate
intact. Show that the chemical will accumulate at a linear rate C(t) = Co+kt.
What is the accumulation rate (value of the constant k)?
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