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But we know that the amount as a function of time-- so if we say N is the amount of a radioactive sample we have at some time-- we know that's equal to the initial amount we have.
We'll call that N sub 0, times e to the negative kt-- where this constant is particular to that thing's half-life.
And now, we can get our calculator out and just solve for what this time is. So this is 1 divided by 1 plus 0.01 divided by 0.11.
And it's going to be in years because that's how we figured out this constant.
And let's say that the argon-- actually, I'm going to say the potassium-40 found, and let's say the argon-40 found-- let's say it is 0.01 milligram. And to figure out our initial amount, we just have to remember that for every argon-40 we see, that must have decayed from-- when you have potassium-40, when it decays, 11% decays into argon-40 and the rest-- 89%-- decays into calcium-40. So however much argon-40, that is 11% of the decay product.
And so we could make this as over 1.25 times 10 to the ninth. If I have a natural log of b-- we know from our logarithm properties, this is the same thing as the natural log of b to the a power.
And we know that there's a generalized way to describe that.
And we go into more depth and kind of prove it in other Khan Academy videos.
In the last video, we give a bit of an overview of potassium-argon dating.
In this video, I want to go through a concrete example.
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