00:01
This is the formula given for the half -life of caffeine.
00:05
And the first question is, how long will it take for the amount of caffeine to drop below 60 milligrams? so this is the amount of caffeine.
00:13
We want that amount to be below 60.
00:21
So this is the equation we are going to solve.
00:30
And i think i'm just going to solve it as it is an equal sign.
00:33
So let's just go with that.
00:34
First, you want to divide both sides by 80.
00:38
So i'll give you 6 over 8 equals 2t to the 6.
00:43
I'm not going to worry about reducing the 6 over 8 here.
00:46
And then we're going to do the natural log of both sides.
00:52
And that is to use the power property of logs to bring this down like so.
01:06
So then we're going to have the natural log of 6 over 8 divided by the, natural log of 2, and that'll equal t over 6.
01:17
And then if we multiply six times this, natural log of 6 over 8, divided by the natural log of 2, that will give us the time that it will take to equal the 60 minutes, and that gives us a time value of negative 2 .5 round to the 10th...