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When blood flows along a blood vessel, the flux $ F $ (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius $ R $ of the blood vessel: $ F = kR^4 $(This is known as Poiseuille's Law; we will show why it is true in Section 8.4.) A partially clogged artery can be expanded by an operation called angioplasty, in which a balloon-tipped catheter in inflated inside the artery in order to widen it and restore the normal blood flow. Show that the relative change in $ F $ is about four times the relative changes in $ R. $ How will a $ 5\% $ increase in the radius affect the flow of blood?

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Missouri State University

Harvey Mudd College

University of Nottingham

Boston College

Lectures

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okay, we know that if at this k r to the fourth and we know that d over d R before kay are cute, Therefore Delta after is four k are few times Delta are Therefore don't ask over K art of the fourth is four k are few times Delta Are you okay? Are before Therefore we have delta half over half is four times delta are over our remember The relative error is four times the relative Aaron are that gives us f Therefore, we know that we would have a percentage error for our 5% there for bath would be five times for which would give us 20%.

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Baylor University

University of Michigan - Ann Arbor

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