related rates calculus problem?

a heart attack victim has been given a blood vessel dilator drug to lower the pressure. for a short while after the drug is given, the radii of the blood vessels will increase by about 1% of the radius/min. According to Poiseuille's Law V=k r^4, what percentage rate of increase can we expect in the blood flow?

but i need the answer using related rates and derivatives please.

another answerer said:

for the second question on the blood flow rate, what is not clear to me, and maybe you have a better answer on this (if your specialty is in biology, pharmaceuticals or medicine), is if the increase in the radii of a blood vessel due to the dilator drug follows a population increase model (like in question 1) or a linear increase model. What I found out in either case outlined below, the rate of increase in blood flow is the same within a given level of accuracy for the first few minutes. to highlight this follow:

Population increase mode (or exponential increase):

r(t) = r0 * (1.01)^t, where r0 is the initial radii of a blood vessel.

V(t) = k * r(t)^4 = k * (r0 * (1.01)^t )^4

= k * r0^4 * (1.01)^(4t)

you can think of V0=k*r0^4 as the initial blood flow level before the drug is applied

therefore,

V(t) = V0 * (1.01)^(4t)

and the second term is the increase

Percentage Increase = ((1.01)^(4t) - 1)*100

For linear model:

r(t) = r0 * (1+0.01*t), where r0 is the initial radii of a blood vessel.

V(t) = k * r(t)^4 = k * (r0 * (1+0.01*t))^4

= k * r0^4 * (1+0.01*t)^4

you can think of V0=k*r0^4 as the initial blood flow level before the drug is applied

therefore,

V(t) = V0 * (1+0.01*t)^4

and the second term is the increase

Percentage Increase = ((1.01)^(4t) - 1)*100

For the first few minutes, both models will give similar results.

t (min) %

0 0%

1 4%

2 8%

3 13%

4 17%

5 22%