The volume of blood flowing through an artery whose radius is r is proportional to the fourth power of the radius.
(a) Suppose there is a 15% increase in the radius of the artery, what is the corresponding percentage increase in the volume of the blood flowing through it?
(b) Show that for a relative change in the radius of the artery, there is a fourfold increase in the volume of blood flowing through it (Physicians exploit this relationship between the volume of blood flowing and the radius of the artery. By slightly increasing the radius of an artery they are able to obtain a significant increase in blood flow.)