00:01
So in this problem, we're treating patients with iodine 131, also written 131 over i, like that in parentheses.
00:10
And the trick about this is this is a radioactive substance, and so it has a radioactive half -life of eight days.
00:19
It has a biological half -life of 4 .2 days, meaning in our body, it's only there, well, it degrades to half of its amount in 4 .2 days.
00:30
And notice that's lower than the eight days because of excretion and other ways for it to leave the body.
00:39
So with that, a person that's treated with 200 milliliters of 131 iodine, their radioactivity amount of iodine in their body are follows this curve, 200 times 2 to the negative t over 4 .2.
01:00
And so by law, they have to stay in the hospital for two days after this treatment.
01:05
So at the end of two days, how much do we have? well, we have that r is 200 times 2 to the negative 2 over 4 .2.
01:18
Okay.
01:21
And so we take 2 to the parentheses negative 2 divided by 4 .2 power.
01:38
Times 200 to the right c's so this would be 200 times 2 to the negative 0 .47619 so in my calculator i take 2 to the 0 .47619 and so this is 200 times 619 plus or minus and so this is 200 times 0 .71619 plus or minus and so this is 200 times 0 .000 1 .71887, which is 143 .77.
03:48
We're supposed to do it to the nearest whole unit, which would be 144 after two days.
03:58
All right.
03:59
So then they're supposed to stay isolated until we reaches 22 milliliters of 131.
04:25
Okay, so that means i have 22 is equal to 200 times 2 to the negative t over 4 .2.
04:35
And i need to figure out what t is...