00:01
So in this problem, we're told that the half -life of this substance is equal to 28 years, and we know initially we have 90 milligrams.
00:07
We want to know how long it's going to take for there to only be 64 .8 milligrams remaining.
00:12
Well, we can use our half -life formula.
00:14
This is what it looks like.
00:15
A of t, the amount after two years, is equal to a -sub -zero, the initial amount, times one -half, because it's a half -life, raised to the t, the number of years, divided by n, which is the half -life time.
00:27
So let's fill in what we know.
00:29
Well, we're trying to figure out the time it's going to take for there to be 64 .8 milligrams left.
00:34
So that will be our a of t value.
00:37
A sub zero is the initial amount, which there were 90 milligrams initially.
00:42
Then we're going to have one half.
00:43
Now, we don't know the amount of time, that's t, but we know that our half -lifetime is 28 years.
00:48
So that's our end value.
00:49
So now, all we need to do is solve this equation for t.
00:53
So to begin, i'm going to divide both sides of the equation by 90...