Question

Carbon-14 has a half-life of 5700 years. The charcoal from a tree killed in the volcanic eruption that formed Crater Lake in Oregon contained 59.5% of the carbon-14 found in living matter. What is the approximate the age of Crater Lake?

Answer 1

See below.

Explanation:

Based on the given information, you would set up the following equation:

`(1/2)^x = 0.595`

Then, you would find x:

`log ("base 0.595") 1/2 = x`
`x = 0.749`

This is the number of half-lives that has passed. Since each half-life is 5700 years based on the given information, we can use dimensional analysis to get the answer in years:

`0.749 " half-lives"((5700 " years")/(1 " half-life")) = 4269 " years"`

Therefore, the age of Crater Lake is 4,269 years.

I hope that helps!