A certain drug is being administered intravenously to a hospital patient. mg Fluid containing 1 of the drug enters the patient's bloodstream cm³ cm³ at a rate of 100 The drug is absorbed by body tissues or h otherwise leaves the bloodstream at a rate proportional to the amount present, with a rate constant of 0.5 h¹. (a) Assuming that the drug is always uniformly distributed throughout the bloodstream, write a differential equation for the amount of drug that is present in the bloodstream at any time. Let M(t) be the total amount of the drug (in milligrams) in the patient's body at any given time t (in hours). NOTE: Use M as M(t). dM mg =1000.5 M dt h (b) How much of the drug is present in the body after a long time? NOTE: Enter an exact answer. M = 200 mg ✔
A certain drug is being administered intravenously to a hospital patient. mg Fluid containing 1 of the drug enters the patient's bloodstream cm³ cm³ at a rate of 100 The drug is absorbed by body tissues or h otherwise leaves the bloodstream at a rate proportional to the amount present, with a rate constant of 0.5 h¹. (a) Assuming that the drug is always uniformly distributed throughout the bloodstream, write a differential equation for the amount of drug that is present in the bloodstream at any time. Let M(t) be the total amount of the drug (in milligrams) in the patient's body at any given time t (in hours). NOTE: Use M as M(t). dM mg =1000.5 M dt h (b) How much of the drug is present in the body after a long time? NOTE: Enter an exact answer. M = 200 mg ✔
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
create a detailed solution for 7his
Transcribed Image Text:A certain drug is being administered intravenously to a hospital patient.
mg
Fluid containing 1
of the drug enters the patient's bloodstream
cm³
cm³
at a rate of 100
The drug is absorbed by body tissues or
h
otherwise leaves the bloodstream at a rate proportional to the amount
present, with a rate constant of 0.5 h-¹.
(a) Assuming that the drug is always uniformly distributed throughout
the bloodstream, write a differential equation for the amount of
drug that is present in the bloodstream at any time.
Let M(t) be the total amount of the drug (in milligrams) in the
patient's body at any given time t (in hours).
NOTE: Use M as M (t).
dM
mg
=1000.5 M
✓
dt
h
(b) How much of the drug is present in the body after a long time?
NOTE: Enter an exact answer.
M
= 200
mg ✔
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
