Research done in the 1930s by the French physiologist Jean Poiseuille showed that the resistance R of a blood vessel of length l and radius r is where k is a constant.Suppose a dose of the drug TPA increases r by 22%.How will this affect the resistance R? Assume that l is constant.

Question

Research done in the 1930s by the French physiologist Jean Poiseuille showed that the resistance R of a blood vessel of length l and radius r is  where k is a constant.Suppose a dose of the drug TPA increases r by 22%.How will this affect the resistance R? Assume that l is constant.

Quizplus · Accepted Answer

Using the given formula, R = (8kl)/(pi*r^4), we can see that an increase in r will cause a decrease in R. 
Let the original resistance be R1 = (8kl)/(pi*r^4). 
After the drug TPA increases the radius by 22%, the new radius is 1.22r. 
The new resistance is R2 = (8kl)/(pi*(1.22r)^4). 
Dividing R2 by R1, we get R2/R1 = ((1.22)^4). 
R2/R1 = 1.88. 
Therefore, R2 = 1.88R1. 
This means that R2 is 88% of R1, or a decrease of 12% in resistance. So, the choice is D.

Research Done in the 1930s by the French Physiologist Jean