In my previous question I asked Please explain C14 half-life The OP mentioned that I was thinking of linear decay and C14 was measured in exponential decay.
As I understand it, C14 is always in a state of decay. If we know the exact rate of decay then shouldn't it be linear?
How do we know that C14 decay's exponentially compared to linear and have there been any studies to verify this?
Answer
It's also worth noting that there is nothing special about atoms.
If you have any system where in every period of time an event has a certain chance of happening which only depends on internal effects of the object and no memory or communications with others - you will get the same decay curve. It's purely a matter of the statistics.
If you have a handful of coins and every minute toss them all and remove all the heads into a separate pile - the number of coins remaining in the hand will decay with a half-life of 1 minute.
What is special about carbon14 - and why it is useful for archeaology is that new carbon14 is being made all the time in the atmosphere, and while you are alive you take in this new carbon so the decays don't have any effect until you die. It's like tossing the coins, but while you are alive adding new random coins after each toss - but then when you die have somebody else start to remove the heads. If you assume you died with an equal number of heads and tails, you can work out how many tosses have happened since you died - and so how long ago the sample died.
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