# calculus

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A heart attack victim is given a blood vessel dilator to increase the radii of the blood vessels. After receiving the dilator, the radii of the affected blood vessels increase at about 1% per minute. According to Poiseulle's law, the volume of blood flowing through a vessel and the radius of the vessel are related by the formula V = kr^4 where k is a constant. What will be the percentage rate of increase in the blood flow after the dilator is given?

• calculus -

dV/dt = k d/dt (r)^4 = 4k r^3 dr/dt

(dr/dt)/r = .01
so
dV/dt = 4 k r^3 (.01 r) = .04 k r^4
but we want dV/dt/V times 100

(dV/dt)/V = .04 kr^4/kr^4 = .04
.04 * 100 = 4%

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