00:01
So we're told that a certain radioactive element is a half -life of 38 hours.
00:12
And we want to know two things.
00:14
The first thing we do is figure out how long does it take for 90 % of the radioactivity to be dissipated? so 90 % is gone, which means we have 10 % left.
00:30
So let's think about our function here.
00:33
So f of t is equal to, now our form is this, n0, 1 1 half, to the t over t 1 half.
00:43
So this t 1 half, this is the time for half life.
00:47
The time for half life.
00:48
In this case, it's 30 hours.
00:50
And since we're dealing with percentages, our n0, we'll just call that 1 for 100%.
00:55
So this simplifies to 1 half, t over 38.
01:01
And we want to see when does this equation, equal 10 % of 0 .1.
01:06
So we solve this for t.
01:07
So let's go and apply logarithms.
01:09
Natural log is a nice one to work with.
01:12
Natural log of 0 .1, natural log of 1 half raised to the t over 38...