Explanation Given information: The function is R = k l r 4 and value of Δ r is 10%. Where, R, r and l is the resistance, radius and length of the blood vessel. k and l are constant. Δ r is the increase in the radius of the blood vessel. Formula used: d R = R ′ Δ r (1) Where, d R is change in resistance of the blood vessel. R ′ is the differential of the function R Δ r is the increase in radius r. Calculation: The given function is, R = k l r 4 Differentiate above function and get the value of R ′ . R ′ = − 4 k l r 5 ( ∵ d x n d x = n x n − 1 ) Substitute − 4 k l r 5 for R ′ in equation (1). d R = − 4 k l r 5 Δ r (2) Assume radius of the blood vessel initially was r

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Differential Equations

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Chapter 3.7, Problem 33E

To determine

To calculate: The resistance R of the blood vessel when radius r of the blood vessel is increased by 10%.

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Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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The resistance R of the blood vessel when radius r of the blood vessel is increased by 10%.

Solution Summary: The author calculates the resistance R of the blood vessel when radius r is increased by 10%.

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To calculate: The resistance R of the blood vessel when radius r of the blood vessel is increased by 10%.

Chapter 3 Solutions