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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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