00:01
That a radioactive substance is going to decay exponentially.
00:04
We know we initially have 100 milligrams, and that after 31 hours, there's only 50 milligrams left.
00:09
So what we want to figure out is how many milligrams are going to remain after 45 hours.
00:15
Well, the first thing we need to figure out is our rate of decay.
00:18
Well, luckily, we have an exponential function to help us.
00:21
It's f of x.
00:23
Or actually, you know what? i'm going to do a of t instead.
00:25
So the amount after t hours, so a of t equals a, subsection.
00:30
0, the initial amount, times 1, because it's decaying, minus r, that would be our rate, all raised to the t power.
00:37
So what we need to do is figure out the rate.
00:40
Well, because we know there's 50 milligrams after 31 hours, a of t will equal to 50.
00:45
A sub 0 is the initial amount, which is 100, and then we'll have 1 minus r.
00:50
And for our t value, that would be the amount of hours, which is 31.
00:54
So now we can use this equation to solve for r.
00:57
So the first thing we're going to do is divide both sides of our equation by 50.
01:01
Well, 50 divided by 100 is 1 half.
01:04
So we'll have 1 1ā2.
01:05
So i'm going to take the quantity of 1 minus r to the 31st power...