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 now let's think about a situation-- now that we've figured out a k-- let's think about a situation where we find in some sample-- so let's say the potassium that we find is 1 milligram. And usually, these aren't measured directly, and you really care about the relative amounts.But let's say you were able to figure out the potassium is 1 milligram.So the negative natural log of 1/2 is the same thing as the natural log of 1/2 to the negative 1 power. Anything to the negative power is just its multiplicative inverse. So negative natural log of 1 half is just the natural log of 2 over here. It's essentially the natural log of 2 over the half-life of the substance.So we could actually generalize this if we were talking about some other radioactive substance.