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!

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

 

 

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 (t_1/2) from the rate constant.