# Question #3f7bf

##### 2 Answers

c) 22920 years

#### Explanation:

I am not 100% on this solution, so someone more knowledgeable than I should definitely feel free to jump in and correct if and where necessary.

**Assumption** : The question doesn't make sense if *increased* in the sample - impossible. Therefore I have assumed that the question meant that the ratio

Given the above assumption we have this:

Where subscript *s* denotes the sample's ratio and *c* the current ratio.

The question then is: how many half lives are required to reduce the ratio by that factor. Mathematically that can be expressed like this:

*x* is the number of half lives.

The question provides the half life of carbon-14, so we multiply the number of half lives by the time for each half life to determine the total length of time:

This is not exactly equal to either of the four options (not ideal!), but it is closest to option (c) 22,920 years.

(c) 22,920 years

#### Explanation:

If the ratio of

Then use this equation:

Remember that tthe decay constant, λ is given by:

Then the equation becomes:

Substitute in the values:

Option (c) is closest to this value, so that is the solution.