The half life for radioactive decay of `.^(14)C` is 5730 years. An archaeological artifact containing wood had only `80%` of the `.^(14)C` found in a living tree. Estimat the age of the sample.

Explanation

To estimate the age of the archaeological artifact containing wood with only 80% of the carbon-14 found in a living tree, we can follow these steps:

### Step 1: Understand the Given Data
- Half-life of Carbon-14 (\(T_{1/2}\)) = 5730 years
- Remaining Carbon-14 in the artifact = 80% of the original amount

### Step 2: Convert Percentage to Decimal
- 80% can be expressed as a decimal:
...