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Wave 105 Dating believe that the best relationships in life don’t come from having perfectly filtered profile pictures but actually come from great conversations.Start slowly with a chat online for a few days, get to know each other and once you’re confident enough to meet up for real – get out there and enjoy yourself on a date night! There’s no science involved, or massive questionnaires to fill out - just a great place to meet people.How do we figure out how old this sample is right over there? And we learned that anything that was there before, any argon-40 that was there before would have been able to get out of the liquid lava before it froze or before it hardened. Let's see how many-- this is thousands, so it's 3,000-- so we get 156 million or 156.9 million years if we round.Well, what we need to figure out-- we know that n, the amount we were left with, is this thing right over here. And that's going to be equal to some initial amount-- when we use both of this information to figure that initial amount out-- times e to the negative kt. So to figure out how much potassium-40 this is derived from, we just divide it by 11%. And this isn't the exact number, but it'll get the general idea. So this is approximately a 157-million-year-old sample. ‘Mature dating’ has become a euphemism for dry and boring, but once you get to a certain age, generic dating apps aren’t fun places to date either. Welcome to Lumen - the dating app designed just for you. But they are dull, and boring and they just don’t represent the single over 50s we know.Or I could write it as negative 1.25-- let me write times-- 10 to the ninth k. Or you could view it as multiplying the numerator and the denominator by a negative so that a negative shows up at the top. The negative natural log-- well, I could just write it this way.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.
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.
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.
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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.