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
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy
Problem 4EA: EXERCISES The following table gives the life expectancy at birth of females born in the United...
Related questions
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
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Recommended textbooks for you
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning