00:01
Hi there, so for this problem we're given this expression that is the concentration.
00:07
For part a of this problem, we are asked about how long does it take for the drug to reach the peak concentration? and what is the peak concentration? now what we need to do to obtain this is to derive this expression with respect to time, set that equal to zero, and solve for the time.
00:27
So we derive this with respect to time.
00:30
As you can see, this is the product between two functions.
00:34
So first, we divide the first function, which is the time.
00:39
So that will be just simply 20 times the exponential of minus 0 .03 times the time.
00:46
And now we leave as a constant the time and they divide the exponential.
00:52
So that will be minus 0 .03.
00:58
Times 20 and this times the time, this times the exponential of minus 0 .03 times the time, and then we set this equal to 0.
01:09
We can cancel the exponential with the exponential, then solving for the time that will be 20 divided by, yes, 20 divided by 0 .03, and this times 20.
01:27
We can count.
01:27
Cancel the 20 with the 20, so that will be 1 divided by 0 .03.
01:34
Then using our calculator, we obtain a value of 33 .3 minutes.
01:59
So that's the solution for the first part of part a of this problem.
02:03
Now for the second question, we are asked about the peak concentration.
02:07
Now, what we need to do is to do.
02:10
To just simply evaluate the concentration at this value, 33 .3 .3.
02:17
And then this is equal to 20 times 33 .3.
02:25
And this times the exponential of minus 0 .03 times 33 .3.
02:38
Then using our calculator, we obtain a value of 245 .25.
03:08
And this in units of nanograms per milliliter...