# Half-Lives (Chemistry)

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Q: If it takes 24 days for 75% of an isotope to undergo a first order decay reaction what is the half-life for the isotope?

I understand half-lives, however, I'm just not sure what the question is asking for me to solve. I thought it meant that 75% of an element (that happened to be an isotope of an element) took 24 days to decay by 75%, meaning 25% was still left. So I thought I would figure out the original amount of time it took at that rate, which would be 32 days. Then I halved that (because it is the half life of it) and got 16 days, however, that is not an answer choice.

I don't know if there is a formula to solve this, but this has got me quite confused for the last 30 minutes or so. Please help, thanks!

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Half life is exponential, not linear, like Cellular reproduction and such, so it is not that simple.

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An equation for exponential decay is A(t) = A0e(-kt).  I would use the information in the problem to calculate the rate constant k, then I would calculate the half-time (t1/2) from the rate constant.

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