calculus

posted by .

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%

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. salt blood pressure

    Why does an increased salt intake cause a rise in blood pressure in salt sensitive individuals?
  2. Body System

    The cardiovascular system consists of A. blood, blood vessels, heart, lymph, lymph vessels, and lymphatic tissues. B. heart, blood vessels, and lymph vessels. C. blood, blood vessels, and heart. D. heart and coronary arteries. The …
  3. biology

    After a meal rich in starch, the blood with the highest concentration of sugar would be in what blood vessel?
  4. biology

    After a meal rich in starch, the blood with the highest concentration of sugar would be in what blood vessel?
  5. Physics

    How much higher must your blood pressure get to compensate for a 5% narrowing in your blood vessels?
  6. Physics

    Smoking causes blood vessels to constrict. If the average blood vessel radius of a smoker decreases 7.6% and the body increases blood pressure to maintain a constant flow. Calculate the needed percent increase in pressure.
  7. Calculus Help Please!!!

    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 = kR4 (This is known as Poiseuille's Law.) …
  8. helth plz help

    the blood vessels that carry blood away from the heart to the rest of the body are… plasma ****** red blood cells whight blood cells platelets 4.Which component of blood is used to help create a scab after you cut your finger?
  9. Math

    The blood vascular system consists of blood vessels (arteries, arterioles, capillaries, and veins) that convey blood from the heart to the organs and back to the heart. This system should work so as to minimize the energy expended …
  10. Math

    The blood vascular system consists of blood vessels (arteries, arterioles, capillaries, and veins) that convey blood from the heart to the organs and back to the heart. This system should work so as to minimize the energy expended …

More Similar Questions