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So you get 1 over this quantity, which is 1 plus 0.01 over the 11%. And then, if you want to solve for t, you want to take the natural log of both sides. And then, to solve for t, you divide both sides by negative k. And you can see, this a little bit cumbersome mathematically, but we're getting to the answer. The mathematics really is something that you would see in high school.
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.And it's going to be in years because that's how we figured out this constant. Ngauruhoe in the Taupo Volcanic Zone, produced andesite flows in 19 and avalanche deposits in 1975.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.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.