Preview Activity 8.2.1. 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 5 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, 8% 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. a. Explain why Q(1) = 5 × 0.08 mg. b. Explain why Q(2) = (5 + Q(1)) × 0.08 mg. Then show that Q(2) = (5 × 0.08) (1 +0.08)mg. c. Explain why Q(3) = (5 + Q(2)) × 0.08 mg. Then show that Q(3) = (5 × 0.08) (1 + 0.08 + 0.08²)mg. d. Explain why Q(4) = (5 + Q(3)) × 0.08 mg. Then show that Q(4) = (5 × 0.08) (1 + 0.08 +0.08² +0.08³) mg. e. There is a pattern that you should see emerging. Use this pattern to find a formula for Q(n), where n is an arbitrary positive integer. f. Complete Table 8.2.1 with values of Q(n) for the provided n-values (reporting Q(n) to 10 decimal places). What appears to be happening to the sequence Q(n) as n increases? Table 8.2.1. Values of Q(n) for selected values of n 2 3 4 5 6 7 8 9 10 1 Q(n) 0.40 n
Preview Activity 8.2.1. 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 5 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, 8% 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. a. Explain why Q(1) = 5 × 0.08 mg. b. Explain why Q(2) = (5 + Q(1)) × 0.08 mg. Then show that Q(2) = (5 × 0.08) (1 +0.08)mg. c. Explain why Q(3) = (5 + Q(2)) × 0.08 mg. Then show that Q(3) = (5 × 0.08) (1 + 0.08 + 0.08²)mg. d. Explain why Q(4) = (5 + Q(3)) × 0.08 mg. Then show that Q(4) = (5 × 0.08) (1 + 0.08 +0.08² +0.08³) mg. e. There is a pattern that you should see emerging. Use this pattern to find a formula for Q(n), where n is an arbitrary positive integer. f. Complete Table 8.2.1 with values of Q(n) for the provided n-values (reporting Q(n) to 10 decimal places). What appears to be happening to the sequence Q(n) as n increases? Table 8.2.1. Values of Q(n) for selected values of n 2 3 4 5 6 7 8 9 10 1 Q(n) 0.40 n
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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Question
Only need help with part d, e and f please. Thank you!
Transcribed Image Text:Preview Activity 8.2.1. 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 5 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, 8% 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.
a.
Explain why Q(1) = 5 × 0.08 mg.
b. Explain why Q (2)
(5+Q(1)) × 0.08 mg. Then show that
Q(2) = (5 × 0.08) (1 + 0.08)mg.
(5+Q(2)) × 0.08 mg. Then show that
Q(3) = (5 x 0.08) (1+0.08 +0.08²) mg.
c. Explain why Q (3)
=
=
d. Explain why Q(4) = (5 + Q(3)) × 0.08 mg. Then show that
Q(4) = (5 × 0.08) (1 +0.08 +0.08² + 0.08³)mg.
e. There is a pattern that you should see emerging. Use this pattern to find
a formula for Q(n), where n is an arbitrary positive integer.
f. Complete Table 8.2.1 with values of Q(n) for the provided n-values
(reporting Q(n) to 10 decimal places). What appears to be happening to
the sequence Q(n) as n increases?
Table 8.2.1. Values of Q(n) for selected values of n
n
1 2 3 4 5 6 7 8 9 10
Q(n) 0.40
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