Carbon-14 is radioactive and has a half-life of 5,700 years.
The number of radioactive carbon-14 atoms in a very old piece of wood is found to have decreased from 1,000,000 to 125,000.
Determine the age of the piece of wood.
so keep dividing 1,000,000 by 2 until you get to 125,000 i think, so that would be 3, therefore 3 half lives. So if one half life is 5,700 i think you would just multiply that by 3 to get 17100 years. might be wrong.
The half-life is defined as the time taken for the activity of a radioactive substance to halve. This is constant no matter how much of it was there to begin with. Radioactivity is an exponential decay because the number of decays occurring per second is proportional to how many nucleons there are of it. So after 1 half-life, it's down to 500,000. Then another half-life passes and it's down to 250,000. Then another half-life passes and it's down to 125,000. So with n half-lives that pass, the number of radioactive nuclei is multiplied by (0.5)n
Just as an extra bit:
You could generalise this as where n is the number of half-lives that have passed and N0 is how many there were to begin with. If you don't have an integer number of half-lives then you'd have to fiddle with logarithms but this only matters in A-level physics.