Question

What is the fraction of a sample of carbon-14 left after 22,800 years if its half life is 5,700 years?

Answer 1

One sixteenth of the original amount.

Explanation:

After each half life period the amount of carbon 14 decays radioactively by a half, therefore you have:

After 1 half life: 50%
After 2 half lives: 50% of 50% = 25%
After 3 half lives: 50% of 25% = 12.5%
After 4 half lives: 50% of 12.5% = 6.25%

22,800 is exactly 4 half lives, so the amount remaining is 6.25% or one sixteenth.