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Relative change in blood flow Another law of Poiseuille says that when blood flows along a blood vessel, the flux $F$ (the volume of blood per unit time that flows past a givenpoint) is proportional to the fourth power of the radius $R$ of the blood vessel:$$F=k R^{4}$$(We will show why this is true in Section $6.3 . )$ A partially clogged artery can be expanded by an operation called angioplasty, in which a balloon-tipped catheter is 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 change in $R .$ How will a 5$\%$ increase in the radius affect the flow of blood?

20$\%$

Calculus 1 / AB

Chapter 3

Derivatives

Section 8

Linear Approximations and Taylor Polynomials

Missouri State University

Harvey Mudd College

Idaho State University

Boston College

Lectures

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In mathematics, a derivati…

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When blood flows along a b…

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Relative change in blood v…

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Blood flow One of Poiseuil…

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Poiseuille's Law Acco…

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One of Poiseuille's l…

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In the human body, blood v…

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this question asked us to show the relative change in office about four times the relative change in, or we know that the law we're gonna be using as f is k times R to the power of four. Therefore, the relative change and f is gonna be for exponents becomes our coefficient. Times Delta are divided by our delta are over. Our is the relative change in our therefore. What this means is that the relative change in F is equivalent to the relative change in our times four. Therefore, if the radius increases by 5% then flow will be 5% times four. So, Flook, this flow would be 20%.

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