00:01
So we know that r is essentially the rate of volume of blood pumped by the heart per unit of time, which is in liters per minute.
00:10
And that c .a .t is the concentration of dye in milligrams per liter pumped out at a short regular time intervals.
00:19
So that means, essentially what that means is r.
00:24
R.
00:27
C .a .t.
00:27
This first part of the thing is the rate of volume of die flowing out of the heart.
00:52
This is because, again, if r represents the volume of blood pumped out of the heart and we're just, and cet is the concentration of the dye, and we put those together, we're just saying this is the amount of die going out of the heart, which is what this right here represents.
01:05
Now for the next part where it says delta t, oh, this is for part eight, for the next part of this question where delta t, we know that delta t is the change in t, which is time.
01:20
So, to conclude r c of t, delta t equals the flow of the flow of die over the flow of die over.
01:41
The interval and that that would be it the flow of die over the interval out of the heart if we're getting very specific this was this is what r c of t of delta t really represents now for part b let's do that may erase this all right so for part b we are tasked with so okay so just start part b let's do this so b and the net flow between t zero and t one or time the flow but the net flow between t equals zero equals zero and t equals capital t that would just be zero t r c t from what we found uh in part a what this represents and then just using our integral rules we can just take out the coefficient r, 0, t, and then c, t, d, t.
03:01
So that would be the first part.
03:03
And if t is great enough that all the dye is pumped through the heart, the net flow is equal to all of the die.
03:13
Therefore, what that really just means is what the question asks.
03:17
This means that a is equal to, a is equal to r.
03:25
R t0, c, t, d, t...