Warfarin is an anticoagulant that prevents blood clotting; often it is prescribed to stroke victims in order to help ensure blood flow. The level of warfarin has to reach a certain concentration in the blood in order to be effective. Suppose warfarin is taken by a particular patient in a 4 mg dose each day. The drug is absorbed by the body and some is excreted from the system between doses. Assume that at the end of a 24 hour period, 6% of the drug remains in the body. Let Q(n) be the amount (in mg) of warfarin in the body before the (n+1)st dose of the drug is administered. Complete the following table. Q(1) = 4(100) mg Q(2) = 4( 6 6) (1 + 100 Q(3) = 4(160)(1+ 6 Q(4) = 4 ( 180 ) (1 + 180 + ( 100 )² + ( 100 ) ³) mg Q(5)= mg Q(6) = Q(7) Q(8) Q(9) Q(10) = = 100 mg 6 100 + ( 180 ) ²) mg mg mg mg mg mg Based on this data, estimate the long term amount of warfarin in the body: lim Q(n) n-00 mg
Warfarin is an anticoagulant that prevents blood clotting; often it is prescribed to stroke victims in order to help ensure blood flow. The level of warfarin has to reach a certain concentration in the blood in order to be effective. Suppose warfarin is taken by a particular patient in a 4 mg dose each day. The drug is absorbed by the body and some is excreted from the system between doses. Assume that at the end of a 24 hour period, 6% of the drug remains in the body. Let Q(n) be the amount (in mg) of warfarin in the body before the (n+1)st dose of the drug is administered. Complete the following table. Q(1) = 4(100) mg Q(2) = 4( 6 6) (1 + 100 Q(3) = 4(160)(1+ 6 Q(4) = 4 ( 180 ) (1 + 180 + ( 100 )² + ( 100 ) ³) mg Q(5)= mg Q(6) = Q(7) Q(8) Q(9) Q(10) = = 100 mg 6 100 + ( 180 ) ²) mg mg mg mg mg mg Based on this data, estimate the long term amount of warfarin in the body: lim Q(n) n-00 mg
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Warfarin is an anticoagulant that prevents blood clotting; often it is prescribed to stroke victims in order to help ensure blood flow. The level of warfarin has to
reach a certain concentration in the blood in order to be effective.
Suppose warfarin is taken by a particular patient in a 4 mg dose each day. The drug is absorbed by the body and some is excreted from the system between
doses. Assume that at the end of a 24 hour period, 6% of the drug remains in the body. Let Q(n) be the amount (in mg) of warfarin in the body before the
(n+1)st dose of the drug is administered. Complete the following table.
Q(1) = 4(100) mg
Q(2) = 4 (160) (1 +
Q(3) = 4 (160) (1 +
) = 4 (160) (¹ +
Q(4)
Q(5)
Q(6)
Q(7)
Q(8)
Q(9) =
Q(10)
6
100
6
100
6
100
mg
+
(100)²) mg
+ ( 100 )² + ( 100 ) ³) mg
mg
mg
mg
mg
mg
mg
Based on this data, estimate the long term amount of warfarin in the body:
lim Q(n)
n→∞0
mg
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