I understand that it works by measuring the amount of carbon 14 which has different amounts depending how old the matter is. But how is it known how much carbon 14 there was that long ago? Is it just that is takes x years for this much to decay so 104 x yea ago they figure it out on a simple graph?
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The amount of Carbon 14 in the atmosphere is kept stable due to some reaction in the upper atmosphere involving sunlight. The TL;DR is that we are at a balance where the same amount of Carbon 14 decays in the atmosphere as is created.
Now, plants absorb carbon from the air, and animals absorb carbon by eating plants (or other animals). So any living being constantly replenishes the ratio of Carbon 14. Once they die, however, this cycle stops, and the ratio decreases as C14 decays. This rate of decay isn’t affected by external factors, and while the rate isn’t as simple as “x per year” (its exponential), we do have mathematical formulae that can take a measured ratio and tell you how long its been since the measured thing died.
(One side note is that the amount of C14 in the atmosphere *may* have been different in the past, but we can account for this with ice samples that have air trapped in them. We can date this “old air” in a different way, and then use carbon dating “in reverse” to figure out how much C14 was in the atmosphere at that time)
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