Carbon dating using exponential growth
So the natural log of this is minus 5,730k is equal to the natural log of 1/2. The natural log and natural log of both sides of that. So, you just say that 350 grams is how much I'm ending up with. And if you want to know where it came from, watch the previous video.
The halflife of carbon 14 is 5730 ± 30 years, and the method of dating lies in trying to determine how much carbon 14 (the radioactive isotope of carbon) is present in the artifact and comparing it to levels currently present in the atmosphere.
Above is a graph that illustrates the relationship between how much Carbon 14 is left in a sample and how old it is.
And we saw that they're good if we are trying to figure out how much of a compound we have left after one half-life, or two half-lives, or three half-lives.
We can just take 1/2 of the compound at every period.
I can do this by working from the definition of "half-life": in the given amount of time (in this case, hours.