You get 1 milligram over this quantity-- I'll write it in blue-- over this quantity is going to be 1 plus-- I'm just going to assume, actually, that the units here are milligrams. So you get the natural log of 1 over 1 plus 0.01 over 0.11 or 11% is equal to negative kt. And, you know, Sal, gave this very high-level explanation, and then, you say, oh, well, there must be some super difficult mathematics after that.
But let's say you were able to figure out the potassium is 1 milligram.
So maybe I could say k initial-- the potassium-40 initial-- is going to be equal to the amount of potassium 40 we have today-- 1 milligram-- plus the amount of potassium-40 we needed to get this amount of argon-40. And that number of milligrams there, it's really just 11% of the original potassium-40 that it had to come from. And so our initial-- which is really this thing right over here. This is going to be equal to-- and I won't do any of the math-- so we have 1 milligram we have left is equal to 1 milligram-- which is what we found-- plus 0.01 milligram over 0.11. And what you see here is, when we want to solve for t-- assuming we know k, and we do know k now-- that really, the absolute amount doesn't matter. Because if we're solving for t, you want to divide both sides of this equation by this quantity right over here. We're going to divide that by the negative-- I'll use parentheses carefully-- the negative natural log of 2-- that's that there-- divided by 1.25 times 10 to the ninth. So the whole point of this-- I know the math was a little bit involved, but it's something that you would actually see in a pre-calculus class or an algebra 2 class when you're studying exponential growth and decay.
So you get this side-- the left-hand side-- divide both sides. So it's negative natural log of 2 divided by 1.25. But the whole point I wanted to do this is to show you that it's not some crazy voodoo here.
And it'll get a little bit mathy, usually involving a little bit of algebra or a little bit of exponential decay, but to really show you how you can actually figure out the age of some volcanic rock using this technique, using a little bit of mathematics.
So we know that anything that is experiencing radioactive decay, it's experiencing exponential decay.Lumen is a dating app, specifically designed for over 50s to meet genuine like-minded singles.