A certain drug is being administered intravenously to a hospital patient. mg Fluid containing 6 of the drug enters the patient's bloodstream cm³ 3 cm at a rate of 400 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 0.4 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 dt 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

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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A certain drug is being administered intravenously to a hospital patient.
mg
Fluid containing 6
of the drug enters the patient's bloodstream
cm³
cm³
at a rate of 400
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 0.4 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
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
Transcribed Image Text:A certain drug is being administered intravenously to a hospital patient. mg Fluid containing 6 of the drug enters the patient's bloodstream cm³ cm³ at a rate of 400 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 0.4 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 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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