The half-life for radioactive decay of `""^(14)C` is 5730 y.
An archaelogical artifact contained wood that had
only `80%` of the `""^(14)C` found in living tree.
Estimate the age of the sample.

Explanation

To estimate the age of the archaeological artifact containing wood with only 80% of the original `^(14)C`, we can use the concept of half-life and the first-order kinetics of radioactive decay. Here’s a step-by-step solution:

### Step 1: Understand the half-life
The half-life (T₁/₂) of `^(14)C` is given as 5730 years. This means that every 5730 years, half of the `^(14)C` present in a sample will decay.

### Step 2: Determine the decay constant (K)
The decay constant (K) can be calculated using the formula:
\[ K = \frac{0.693}{T_{1/2}} \]
...