How Does a 3% Increase in Radius Affect Blood Flow?

[tc903]

\(\displaystyle F = k{R}^{4} \)

The flux F is volume of blood per unit time. This is proportional to the 4th power of the radius R of the blood vessel. All I am given is 3% increase in radius will affect blood flow how. I am to find whether is decreases or increase blood flow and by what percent.

\(\displaystyle \lim_{{\theta}\to{{0}^{+}}}\frac{A(\theta)}{B(\theta)} \)

I am given \(\displaystyle \overline{PQ} \) is the diameter of a semicircle. \(\displaystyle \triangle PQR \) is an isosceles triangle. \(\displaystyle A(\theta) \) is the area of the semicircle. \(\displaystyle B(\theta) \) is the area of the triangle. I need to find the limit. I started by listing area of a circle and triangle.

I would need some guidance to start either of these. I may be overthinking. Thank you.

 

[Ackbach]

\(\displaystyle F = k{R}^{4} \)

The flux F is volume of blood per unit time. This is proportional to the 4th power of the radius R of the blood vessel. All I am given is 3% increase in radius will affect blood flow how. I am to find whether is decreases or increase blood flow and by what percent.

Typically, you do a derivative/differential to determine this:

$$\Delta F= 3 k R^3 \, \Delta R.$$

You can say that the flux will increase, but you can't say by how much unless you know the actual value of the radius.