00:01
So let's understand the context of this problem.
00:03
So c, my output represents the caffeine in a certain substance.
00:10
I start with one large cup of coffee is 110 milligrams of caffeine rate.
00:15
I usually have a starting value times my half life.
00:18
So half life is the time it takes for caffeine or the substance to be cut in half.
00:22
It is given by the following formula.
00:24
It drops every six hours.
00:26
How long will it take the caffeine to drop below 50 milligrams? so i want my output to be below 50.
00:33
Okay.
00:34
And my goal is just to get t by itself, just like solve in an equation.
00:38
So first step, i'm multiplying this whole term by 110.
00:41
So i'm going to divide by 110 to both sides.
00:45
Okay.
00:46
And i'm just going to keep this as 5 over 11 because this doesn't simplify in the best way.
00:52
Okay.
00:53
Now how do we get that t down? well, what's the inverse of the exponential function? the logarithmic function...