If I begin with 100 atoms, how many atoms will be left of carbon 12 in 17,190 yrs if the half life of C12 is 5,730 yrs?
It is not possible to answer this on such a small sample, as the disintegration is NOT precise: the half-live is an average of many. On a sample such as this...
Think of flipping six coins: will you get three heads and three tails? No.
But if you flip them 1 million times, you get darn close to half heads, half tails.
You teacher probably didn't want you to think on that issue.
so, if you had a 100 million atoms
Nleft= 100,000,000*(1/2)^(17,190/5,730)
= 12,500,000 or 1/8 of the original amount.
In your silly case, of 100 atoms, you would often get 12, or 13, and a few times get 11, or 14, or fewer still, 10, or 15
Radioactivity is not a precise schedule atom by atom.