00:02
So here we have some questions about the cobalt 60 and its half -life.
00:06
So i've written the half -life equation here that will help us determine different variables.
00:11
So first we're asked, how long will it take cobalt 60 to decrease to 18 % of its original activity? and so what we can do is we can substitute in what we know.
00:21
So here we're calculating a time, so we'll just be solving for t.
00:29
So n -t is going to be the amount.
00:33
Left after the time has passed.
00:35
And so here, because we're measuring percentage of activity, we can just assume we can make these into decimals.
00:41
And so 0 .18 will be the 18 % activity, but it's going to start out at 100 % activity or 1.
00:50
And so n .a is what we start with.
00:52
Then we multiply that by 1⁄2 .t over the half -life.
00:57
And the half -life is 5 .27 years.
01:00
So if we go ahead and solve for this, we can take the log of both sides.
01:13
So log of 0 .18 is going to be equal to t over 5 .27, log of 1⁄2.
01:28
And so then we can isolate t on each side, or on the right side.
01:34
So log of 0 .18 over the log of 1⁄2 times 5 .27...