# Carbon dating and logarithms

Where t is the age of the fossil (or the date of death) and ln() is the natural logarithm function.

If the fossil has 35% of its carbon 14 still, then we can substitute values into our equation.

It doesn't really matter that we don't know the exact amount, we're still trying to solve the same exact way.

## dating nicaragua women - Carbon dating and logarithms

Natural log point 71 is equal to negative, it's very small decimal t, natural log of e, natural log of e is just 1, so to solve this out we just divide by this decimal natural log of .71 divided by .00012 is equal to t.

Finish up plug in your calculator, natural log .71 divided by negative .123, 12 and this gives us around 2854 years.

So what they can do is compare the amount that should be in whatever they're looking at into the amount that's left and using a formula which is the exponential decay formula, they can figure out how old something is.

So for this example what we're going to be looking at is a stick in King Tuts tomb.

When finding the age of an organic organism we need to consider the half-life of carbon 14 as well as the rate of decay, which is –0.693.

For example, say a fossil is found that has 35% carbon 14 compared to the living sample. We can use a formula for carbon 14 dating to find the answer.The ratio of carbon-12 to carbon-14 at the moment of death is the same as every other living thing, but the carbon-14 decays and is not replaced.The carbon-14 decays with its half-life of 5,700 years, while the amount of carbon-12 remains constant in the sample.So now we're solving for a variable and the exponent, whenever we see that, we need to just take the natural log.We take a natural log because it's the base e, we could take the log, but then we'd be left with a log b, so we take the natural log, this is going to make our base to disappear.University of Michigan Runs his own tutoring company Carl taught upper-level math in several schools and currently runs his own tutoring company.

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