Question

You are assigned to improve the blood donation process by reducing the wait time for donors. In order to plan the steps in the process you obtain a model for the flow of blood during the donation process. The following relationship is obtained: F = F0 (1 – C t)
Where F = blood flow rate from donor to collection bag, ml/min
F0 = initial blood flow rate, ml/min, found to have a typical value of 25
C is a constant, determined to be 0.022 min-1
T = time, min
What amount of time should be allowed for the donation if the amount to be collected is 500 ml?

Answer 1

Say B is the amount of blood in ml.

Answer 2

\[\begin{align} B&=\int{F}dt \\&=\int{(F_0-Ct)}dt \\&=F_0t-\frac12 Ct^2 \\500&=25t-\frac12 0.22 t^2\end{align}\]

Answer 3

Can you find t from here?

Answer 4

might be able to

Answer 5

How would You cancel out the t's?

Answer 6

Would I Just subtract 25t to the other side then square root the left side of equation?

Answer 7

It's a quadratic equation. You can't just cancel t. Find t with this formula:
\[at^2+bt+c=0\\then\\t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

Answer 8

\[11t ^{2}-25t+500= 0\]

Answer 9

0.11

Answer 10

\[25+\sqrt{625-(220)}/.22\]

Answer 11

== 205.11

Answer 12

Correct!! There's another value actually :)

Answer 13

so now I just plug that in for t, correct?

Answer 14

That's the T you're looking for.In minutes.

Answer 15

True, thankyou very much. Appreciate it

Answer 16

No probs, I enjoy teaching stuff.

Answer 17

I noticed, was gonna ask if you were a teacher.

Answer 18

Yeah, i'm actually a rookie physics teacher.

Answer 19

gotta start somewhere. How did you know to make into a derivative?

Answer 20

From definition of rate, F=dB/dt
so to find B, we must integrate F with respect to t. As we have done before.