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Calculus / Thomas' Calculus: Early Transcendentals 13 / Chapter 3.11 / Problem 63E

Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass

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Unclogging arteries The formula , discovered by the

Chapter 3, Problem 63E

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Problem 63E

Unclogging arteries The formula , discovered by the physiologist Jean Poiseuille (1797-1869), allows us to predict how much the radius of a partially clogged artery has to be expanded in order to restore normal blood flow. The formula says that the volume V of blood flowing through the artery in a unit of time at a fixed pressure is a constant k times the radius of the artery to the fourth power. How will a 10% increase in r affect V?

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QUESTION:

Problem 63E

Unclogging arteries The formula , discovered by the physiologist Jean Poiseuille (1797-1869), allows us to predict how much the radius of a partially clogged artery has to be expanded in order to restore normal blood flow. The formula says that the volume V of blood flowing through the artery in a unit of time at a fixed pressure is a constant k times the radius of the artery to the fourth power. How will a 10% increase in r affect V?

ANSWER:

Solution:

Step 1 of 2

In this problem, we have to find that the effect in volume if the radius is increased by $10\%$ .

The volume of the blood flowing through an artery is given by $V=k{r}^{4}$ .

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