Answered: Medical evidence shows that a small…

Human Anatomy & Physiology (11th Edition)

11th Edition

ISBN:9780134580999

Author:Elaine N. Marieb, Katja N. Hoehn

Publisher:Elaine N. Marieb, Katja N. Hoehn

Chapter1: The Human Body: An Orientation

Section: Chapter Questions

Problem 1RQ: The correct sequence of levels forming the structural hierarchy is A. (a) organ, organ system,...

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Question

Medical evidence shows that a small change in the radius of an artery can indicate a large change in blood flow. For example, if one artery has a radius only 5% larger than another, the blood flow rate is 1.22 times as large. Further information is given in the table below.

Increase in radius	Times greater blood flow rate
5%	1.22
10%	1.46
15%	1.75
20%	2.07

(a) Use the average rate of change to estimate how many times greater the blood flow rate is in an artery that has a radius 8% larger than another. (Round your answer to three decimal places.)
1.364 times greater

(b) Explain why if the radius is increased by 8% and then we increase the radius of the new artery by 8% again, the total increase in the radius is 16.64%.

x + 8% of x
x + 8/100 X x
x + 0.08x = 1.08x
1.08x + 8% of (1.08x)
1.08x + 8/100 X (1.08x)
1.08x + 0.0864x = 0.1664x = 16.64%

(c) Use parts (a) and (b) to answer the following question: How many times greater is the blood flow rate in an artery that is 16.64% larger in radius than another? (Round you answer to three decimal places.)
1.860 times greater

(d) Answer the question in part (c) using the average rate of change. (Round your answer to three decimal places.)

Expert Solution

Step 1 Part a

Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved

Calculate the rate of change of flow with respect to percentage change in the radius ( $∆$ ) using the formula,

$∆ = \frac{C h a n g e i n f l o w}{C h a n g e i n r a d i u s (i n %)} \dots \dots \dots \dots \dots (1)$ .

Calculate for 5%, 10%, 15% and 20% respectively.

$\begin{array}{rcl} ∆_{1} & = & \frac{1.22 - 1}{5} \\ = & \frac{0.22}{5} \\ = & 0.044 \end{array}$

$\begin{array}{rcl} ∆_{2} & = & \frac{1.46 - 1}{10} \\ = & \frac{0.46}{10} \\ = & 0.046 \end{array}$

$\begin{array}{rcl} ∆_{3} & = & \frac{1.75 - 1}{15} \\ = & \frac{0.75}{15} \\ = & 0.05 \end{array}$

$\begin{array}{rcl} ∆_{4} & = & \frac{2.07 - 1}{20} \\ = & \frac{1.07}{20} \\ = & 0.0535 \end{array}$

Calculate average of the rate of change of flow with respect to percentage increase in radius.

$\begin{array}{rcl} A_{v g} & = & \frac{0.044 + 0.046 + 0.05 + 0.0535}{4} \\ = & \frac{0.1935}{4} \\ = & 0.048375 \end{array}$

Calculate change in flow rate by substituting $∆$ as $A_{v g}$ and Percentage change in radius as 8% in formula 1.

$\begin{array}{rcl} A_{v g} & = & \frac{F l o w - 1}{8} \\ 0.048375 & = & \frac{F l o w - 1}{8} \\ F l o w - 1 & = & 0.387 \\ F l o w & = & 1.387 \end{array}$