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Carbon dating uses an unstable isotope of carbon to find the date of dead substances.

This isotope Carbon-14 has a half life of 5,700 years.

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It's always the same thing and if you're having trouble in going from this step to this step, make sure you know how to do that. We take the natural log of both sides and then we solve for t. Let's say that a specimen has been dead for 10,000 years and I want to know its carbon 14 ratio.

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So that's taking into account all the decays and all that stuff, this is a natural abundance. And that means that as time goes on, the carbon 14 abundance will decrease. So the amount that we've got at our time now is 0.5 times 10 to the -12.

So that means the carbon 14 abundance can tell us how long something's been dead. So let's see how we can use this to do a problem. It's bound to have a carbon 14 ratio that's only 0.5 times 10 to the -12. The initial amount when he died must have been 1.3 because he was interacting with its environment. Alright, so that means that t is going to be, I'm just going to solve this equation real quickly, it's going to be 5700 years times the natural log of 0.5 over 1.3 divided by the natural log of one half.

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