# A sample of wood contains 12.5% of its original carbon-14. What is the estimated age of this sample?

Jun 21, 2017

17,151 years

#### Explanation:

First, we need to know the half life of carbon-14, which is approximately 5,717 years.

A half life is how much time it takes for the sample to decay to half of its original amount. So in 5,717 years, a 1 gram sample of carbon-14 would decay to 0.5 grams.

Similarly, if we start with 100% of a sample , we can keep dividing this number by 2 until we reach 12.5% to find out how many half lives passed.

Remember, when the sample is still 100%, 0 half lives have passed.

% remaining: 100 > 50 > 25 > 12.5

Half lives: -------0------1------2-------3

3 half lives passed.

Multiply the half life of carbon-14 (5,717 years) by how many half lives passed.

$5 , 717 \cdot 3 = 17 , 151$

It took 17,151 years for carbon-14 in this sample of wood to reach 12.5%. Therefore, the estimated age of this sample is 17,151 years old.

(Note: if your teacher or reference table states a different half life for carbon-14, use that number instead of 5,717.)