A certain drug is being administered intravenously to a hospital patient. mg Fluid containing 2 of the drug enters the patient's bloodstream cm³ cm at a rate of 500 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

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Show full solution. Answer (a) and (b).

(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:(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
cm ³
at a rate of 500
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
Transcribed Image Text:A certain drug is being administered intravenously to a hospital patient. Fluid containing 2 mg of the drug enters the patient's bloodstream cm³ cm ³ at a rate of 500 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
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