00:01
In this question, the percentage of alcohol in the bloodstream t hours after drinking whiskey is given by the function a, where t is between 0 and 12.
00:11
And we are asked to determine the time when the concentration is the highest and determine the percentage of alcohol.
00:21
So, in other words, we are asked to find the absolute maximum of the function a over the closed interval.
00:30
And the only points where the absolute maximum can occur are either the endpoints, in our case t equals 0 and t equals 12, and the critical points.
00:53
Recall that the critical points are the points where a prime of t is 0 or a prime of t is undefined.
01:10
So let's calculate a prime of t.
01:15
A prime of t equals to the derivative of the function a, and by the product rule equals to 0 .2.
01:22
Times e to the negative 0 .40 plus 0 .2t multiplied by the derivative of e which equals to negative 0 .4 times e to the negative 0 .40.
01:39
And we can factor out 0 .2 times e to the negative 0 .40 multiplied by 1 minus 0 .40.
01:53
So that's a prime of t...