00:04
So in this problem were given that we have a model for the infection level of a measles virus in a patient is given by this function f.
00:15
Of t equals minus t.
00:21
Times t -21 times t plus one.
00:31
Where t.
00:31
Is measured in days, tears and days.
00:37
And our f.
00:38
A.
00:38
T.
00:38
Is measured in the number of infected cells.
00:42
Uh huh.
00:47
Affected cells.
00:52
Uh huh.
00:54
Middle leader one plasma drop.
01:03
That's right.
01:03
That little bit neater of one last month.
01:16
Okay.
01:18
And were asked over the 21 day infection.
01:21
What is the average level of infection? okay, so first we consider the infection level.
01:31
Never buy this function.
01:32
Okay, objective is to find the average level.
01:36
So we want to find the average level over the 21 days.
01:51
This is what we're looking for.
01:58
So the average level then f average over this interval from a.
02:12
To b.
02:14
All right.
02:14
Would be one over b minus a.
02:20
I.
02:20
Was integral.
02:22
Ready to be of f.
02:25
Of x.
02:26
D.
02:26
X.
02:29
Okay, so that means this becomes 1/21 because we're doing it over 21 days.
02:42
And this is the interval then from 0 to 21 f.
02:46
Of t.
02:48
D.
02:48
T.
02:50
For what we have.
02:52
Mhm...