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

##### 1 Answer

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.

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.)