And we know that there's a generalized way to describe that.
And we go into more depth and kind of prove it in other Khan Academy videos.
By looking at the ratio of carbon-12 to carbon-14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of a formerly living thing fairly precisely. So, if you had a fossil that had 10 percent carbon-14 compared to a living sample, then that fossil would be: t = [ ln (0.10) / (-0.693) ] x 5,700 years t = [ (-2.303) / (-0.693) ] x 5,700 years t = [ 3.323 ] x 5,700 years Because the half-life of carbon-14 is 5,700 years, it is only reliable for dating objects up to about 60,000 years old.
Potassium-40 is another radioactive element naturally found in your body and has a half-life of 1.3 billion years.
Other useful radioisotopes for radioactive dating include Uranium -235 (half-life = 704 million years), Uranium -238 (half-life = 4.5 billion years), Thorium-232 (half-life = 14 billion years) and Rubidium-87 (half-life = 49 billion years).
But we know that the amount as a function of time-- so if we say N is the amount of a radioactive sample we have at some time-- we know that's equal to the initial amount we have.
We'll call that N sub 0, times e to the negative kt-- where this constant is particular to that thing's half-life.
This convention is necessary in order to keep published radiocarbon results comparable to each other; without this convention, a given radiocarbon result would be of no use unless the year it was measured was also known—an age of 500 years published in 2010 would indicate a likely sample date of 1510, for example.