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The ‘Dating Rule’
The following 2 pages uses this file: The following other wikis use this file: Short title Half age plus seven rule: Width Height Retrieved from " https: Views View Edit History. This page was last edited on 10 January , at By using this site, you agree to the Terms of Use and Privacy Policy. Self-made graphic, with layout partially influenced by the PD image en: The natural log of e to anything, the natural log of e to the a is just a.
I just took the natural log of both sides. The natural log and natural log of both sides of that. But let's see if we can do that again here, to avoid-- for those who might have skipped it. So it equals 1. So now we have the general formula for carbon, given its half-life.
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At any given point in time, after our starting point-- so this is for, let's call this for carbon, for c the amount of carbon we're going to have left is going to be the amount that we started with times e to the minus k. This is our formula for carbon, for carbon If we were doing this for some other element, we would use that element's half-life to figure out how much we're going to have at any given period of time to figure out the k value.
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So let's use this to solve a problem. Let's say that I start off with, I don't know, say I start off with grams of carbon, carbon And I want to know, how much do I have after, I don't know, after years? How much do I have? Well I just plug into the formula. N of is equal to the amount that I started off with, grams, times e to the minus 1. So what is that? So I already have that 1. So let me say, times equals-- and of course, this throws a negative out there, so let me put the negative number out there.
So there's a negative.
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And I have to raise e to this power. So this is equal to N of The amount of the substance I can expect after years is equal to times e to the minus 0.
And let's see, my calculator doesn't have an e to the power, so Let me just take e. I need to get a better calculator. I should get my scientific calculator back. But e is, let's say 2. So this is equal to grams. So just like that, using this exponential decay formula, I was able to figure out how much of the carbon I have after kind of an unusual period of time, a non-half-life period of time. Let's do another one like this. Let's go the other way around. Let's say, I'm trying to figure out. Let's say I start off with grams of c And I want to know how long-- so I want to know a certain amount of time-- does it take for me to get to grams of c?
So, you just say that grams is how much I'm ending up with. It's equal to the amount that I started off with, grams, times e to the minus k. And now we solve for time. How do we do that?
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Well we could divide both sides by What's divided by ? So you get 0. You take the natural log of both sides. You get the natural log of 0.
And so t is equal to this divided by 1.