00:01
In this question, we say that a drug's concentration in a patient's blood in micrograms per milliliter can be modeled by the function c of t, which is 4t over 0 .1t squared plus 3 .9, where t is the time in minutes since the drug is injected.
00:18
In part one, we say, what is the drug's concentration 25 minutes since the injection? we're going to round our answer to two decimal places.
00:26
In number one, we're just going to evaluate c of 25.
00:32
What am i getting? well, up top, i have 4 times 25, that's 100, and then i'm dividing that by 0 .1 times 25 squared, and then to that, i'm going to add 3 .9.
00:52
I have 1 .51.
00:55
Here i'm getting 1 .51.
00:59
That's my answer to question number one.
01:02
Now in question two, when the drug's concentration decreases to 0 .53 milligrams per milliliter, it's time to give the patient another injection.
01:13
How long should the nurse wait before another injection? we'll round to the nearest integer if necessary.
01:20
Now they're giving me a concentration, 0 .53, and i'm going to plug that in for c of t.
01:25
So 0 .53 equals 4t over 0 .1t squared plus 3 .9.
01:36
Now this is a calculator -active question, so what i'm going to do is set this equal to 0 and use the 0 key on my calculator.
01:44
So 0 equals 4t over 0 .1t squared plus 3 .9, and from this, i'm going to subtract 0 .53.
01:53
So let's see...