Question

The half-life of carbon-14 is 5730 years. What percentage of carbon-14 remains in a sample after 7 half lives?

Answer 1

`(frac{1}{2})^7 = 1/128 ~~ 0.781%`

Explanation:

After 1 half-life, `1/2` of the C-14 would remain.

After 2 half-life, `1/2` of the `1/2` of the C-14 = `1/4` of the C-14 would remain.

After 3 half-life, `1/2` of the `1/4` of the C-14 = `1/8` of the C-14 would remain.

...

After `n` half-lives, `frac{1}{2^n}` of the C-14 would remain.