Chapter 1.2, Problem 22E

Reminder Round all answers to two decimal places unless otherwise indicated.

Arterial Blood Flow 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 $12\%$ larger than another.

b. Explain why if the radius is increased by $12\%$ and then we increase the radius of the new artery by $12\%$ again, the total increase in the radius is $25.44\%$.

c. Use parts a and b to answer the following question: How many times greater is the blood flow rate in an artery that $25.44\%$ larger in radius than another?

d. Answer the question in part c using the average rate of change.