A certain drug is being administered intravenously to a hospital patient. Fluid containing 2 mg of the drug enters the patient's bloodstream cm³ cm³ at a rate of 100 h The drug is absorbed by body tissues or otherwise leaves the bloodstream at a rate proportional to the amount present, with a rate constant of 0.2 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 dt mg h NOTE: Check your variables. Use a capital M (b) How much of the drug is present in the body after a long time? NOTE: Enter an exact answer. M mg

A certain drug is being administered intravenously to a hospital patient. Fluid containing 2 mg of the drug enters the patient's bloodstream cm³ cm³ at a rate of 100 h The drug is absorbed by body tissues or otherwise leaves the bloodstream at a rate proportional to the amount present, with a rate constant of 0.2 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 dt mg h NOTE: Check your variables. Use a capital M (b) How much of the drug is present in the body after a long time? NOTE: Enter an exact answer. M mg

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

100%

A certain drug is being administered intravenously to a hospital patient.
mg
Fluid containing 2
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 0.2 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).
d.M
mg
h
dt
NOTE: Check your variables. Use a capital M
(b) How much of the drug is present in the body after a long time?
NOTE: Enter an exact answer.
M =
mg

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