# Exponential decay formula proof

Exponential decay and semi-log plots Video transcript SAL. The notion of a half-life is useful, if we're dealing with increments of time that are multiples of a half-life. So if I say that three half-lives have gone by-- in the case of carbon that would be, what, roughly 15,000 years-- I can tell you roughly, or almost exactly, what percentage of my original element I still have. In the case of carbon-14, I'll tell you what percentage of my original carbon-14 has not decayed into nitrogen, as yet, nitrogen-14. What if I want a general function. A general function, as a function of time, that tells me the number, or the amount, of my decaying substance I have.

## how to calculate half life apes

Exponential decay and semi-log plots Video transcript SAL. Two videos ago we learned about half-lives. And we saw that they're good if we are trying to figure out how much of a compound we have left after one half-life, or two half-lives, or three half-lives. And to address that issue in the last video, I proved that it involved a little bit of sophisticated math.Exponential decay and semi-log plots Video transcript SAL. Let's do a couple more of these exponential decay problems, because a lot of this really is just practice and being very comfortable with the general formula, and I'll write it again. Where the amount of the element that's decaying, that we have at any period in time, is equal to the amount that we started with, times e to the minus kt. Where the k value is specific to any certain element with a certain half-life, and sometimes they don't even give you the half-life.

### half life formula math

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