00:01
So we have a radioactive decay model, and we're told that we start with a sample of 100 grams and decay to 75 grams in 250 years.
00:17
So we're going to use that information to find the decay rate.
00:24
Take the natural log of both sides, use your log properties, and bring your exponent down.
00:32
Ln of e is just 1.
00:37
Divide both sides by 250, and let's get our value for k.
00:43
Ln of 0 .75, then divide by 250, you have negative 0 .00115.
00:52
Now we want to turn that into a percent, so that is going to give me negative 0 .1151 % or 0 .12%, and that's decay.
01:17
Now we want to know how much is left after 400 years.
01:21
We start with 100.
01:23
We know our decay rate is negative 0 .00115, and we're going to put in 400 years.
01:37
Put in 400 for t.
01:43
So raise e to the negative 0 .00115 times 400 power, then multiply by 100...