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# 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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