00:02
Okay, so i am going to get the decay rate, and then we will figure out the half -life.
00:12
So this function is going to follow the law of uninhibited growth slash decay.
00:21
A -0 is my initial amount, so that's 332 in this problem.
00:27
E to the k is what we're solving for, and after 200 ,000, 55 minutes, we have 5 .1875 grams.
00:39
Divide both sides by 332 because we want to isolate that exponential expression.
00:48
I'm divided by 332.
00:51
Now it's going to give me 0 .01562525252 equal to e to the 255k.
01:00
Take the ln of both sides drop your exponent down because you brought in logs you get to use log properties ln of egist equals one and let's get a tk rate so ln .0 .015625 divided by 255 k is negative 0163.
01:40
Okay.
01:42
Now that i have k, i'm going to bring k up here to get the half -life.
01:50
Okay, the half -life is the amount of time it takes for your original amount to decrease to half.
01:57
Now i know that's 0163 negative.
02:04
I can now solve for tick.
02:08
Get rid of a sub zero again i'm going to turn this into point five take your ln again drop that exponent down again ln of v is still one so we are going to find let's do that math we want ln of 0 .5 divided by negative 0 .0163 that time is 42 0 .52 minutes...