When blood flows along a blood vessel, the flux $ F $ (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius $ R $ of the blood vessel:
$ F = kR^4 $
(This is known as Poiseuille's Law; we will show why it is true in Section 8.4.) A partially clogged artery can be expanded by an operation called angioplasty, in which a balloon-tipped catheter in 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 changes in $ R. $ How will a $ 5\% $ increase in the radius affect the flow of blood?
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