Question

The radioactive element​ carbon-14 has a​ half-life of 5750 years. a scientist determined that the bones from a mastodon had lost 56.356.3​% of their​ carbon-14. how old were the bones at the time they were​ discovered?

Answer 1

6870 years Since the bones lost 56.3% of their carbon-14 that means that 43.7% of the carbon-14 is left. So let's determine how many half-lives have expired by calculating the base 2 logarithm of 0.437 log(0.437)/log(2) = -0.359518563 / 0.301029996 = -1.194294815 So we've undergone 1.194 half-lives. This makes sense since if we had undergone exactly 1 half-life, there would be 50% of the original carbon-14 left, and if we had undergone 2 half-lives, there would be 25% left. 43.7% is between those two values and fairly close to the 50% value indicating that a bit more than 1 half-life has expired. So now multiply by the number of half lives expired to get the age, which is 1.194 * 5750 = 6865.5 Since we only have 3 significant figures, rounding gives us 6870 years.