# Carbon dating exponential decay formula

Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the death dates We can use a formula for carbon 14 dating to find the answer.

For a given x , a function gives you the y value. So just as correctly, for a given t , an exponential function can give you the N t.

## More exponential decay examples (video) | Khan Academy

You still need to figure out N 0 and k , though. Let's look carefully at the data points you are given: If the pair is interpreted as t, N 0 then you can see that this is an exponential growth rather than decay because when one of them increased, the other increased.

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3. BioMath: Carbon Dating.

If you substitute the point 0,1 into the equation model, you get:. So that figured out the N 0 value and putting that together with the other data point is all we need to solve for the constant of growth. Meadow Who is Asking: I know that this is some kind of log problem.

We can use exponential decay to represent a number of different things. Most importantly, exponential decay is not linear and the decrease is rapid at first, but not constant.

It is often used to describe population decreases or increases, which depicts exponential growth and can be seen using a graph of an exponential curve. Natasha Glydon Exponential decay is a particular form of a very rapid decrease in some quantity. If P o is the initial amount of pollutants in the kerosene, then the amount left, P , after n feet of pipe can be represented by the following equation: Carbon 14 Dating Archaeologists use the exponential, radioactive decay of carbon 14 to estimate the death dates of organic material. The stable form of carbon is carbon 12 and the radioactive isotope carbon 14 decays over time into nitrogen 14 and other particles.

Carbon is naturally in all living organisms and is replenished in the tissues by eating other organisms or by breathing air that contains carbon.

At any particular time all living organisms have approximately the same ratio of carbon 12 to carbon 14 in their tissues. When an organism dies it ceases to replenish carbon in its tissues and the decay of carbon 14 to nitrogen 14 changes the ratio of carbon 12 to carbon Experts can compare the ratio of carbon 12 to carbon 14 in dead material to the ratio when the organism was alive to estimate the date of its death.

Radiocarbon dating can be used on samples of bone, cloth, wood and plant fibers. And I gave you this, if you have to figure it out from half-life, I did that in the previous video with carbon But let's say this is the formula. And let's say that after, I don't know, let's say after years I have grams of whatever element is described. The decay formula for whatever element is described by this formula.

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• How much did I start off with? So essentially I need to figure out N sub 0, right? I'm saying that after years, so N of , which is equal to N sub naught times e to the minus 0.

## Introduction to exponential decay

That's the N of And I'm saying that that's equal to grams. That equals grams. So I just have to solve for N sub naught. So what's the e value? So if I have 0.

Or I could multiply both sides by e, and I have N sub naught is equal to e, which is about 2. So it's times 2. I don't actually have e on this calculator or at least I don't see it. So we'll have 1, grams. So it's equal to 1, grams, or 1. That's what I started with.

So hopefully you see now. I mean, I think we've approached this pretty much at almost any direction that a chemistry test or teacher could throw the problem at you. But you really just need to remember this formula.

## More exponential decay examples

And this applies to a lot of things. Later you'll learn, you know, when you do compound interest in finance, the k will just be a positive value, but it's essentially the same formula. And there's a lot of things that this formula actually describes well beyond just radioactive decay. But the simple idea is, use information they give you to solve for as many of these constants as you can.

And then whatever they're asking for, solve for whatever's left over. And hopefully I've given you enough examples of that. But let me know, I'm happy to do more.