A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate proportional to the quantity present, with constant of proportionality k > 0. (a) Set up a differential equation for the quantity, Q, in milligrams, of the drug in the body at time t hours. Your answer will contain the unknown constants r and k. Q' = r-kQ (b) Solve this differential equation, assuming there is no drug in the body initially. Your answer will contain r and k. = 7/1 (1 - e-kt) (c) What is the limiting long-run value of Q? lim Q(t) t→∞0 = r k

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question

I need help with an expliantion in how I got these answer and why?

A drug is administered intravenously at a constant rate of r mg/hour and is
excreted at a rate proportional to the quantity present, with constant of
proportionality k > 0.
(a) Set up a differential equation for the quantity, Q, in milligrams, of the drug in
the body at time t hours. Your answer will contain the unknown constants r and k.
Q' = r-kQ
(b) Solve this differential equation, assuming there is no drug in the body initially.
Your answer will contain rand k.
=
/ 1 (1 - e-ht)
(c) What is the limiting long-run value of Q?
lim Q(t)
0077
=
r
k
Transcribed Image Text:A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate proportional to the quantity present, with constant of proportionality k > 0. (a) Set up a differential equation for the quantity, Q, in milligrams, of the drug in the body at time t hours. Your answer will contain the unknown constants r and k. Q' = r-kQ (b) Solve this differential equation, assuming there is no drug in the body initially. Your answer will contain rand k. = / 1 (1 - e-ht) (c) What is the limiting long-run value of Q? lim Q(t) 0077 = r k
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 4 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,