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. Estimate the age of the sample.

Explanation

To estimate the age of the archaeological artifact containing wood with only 80% of the original carbon-14, we can use the principles of radioactive decay and the half-life of carbon-14. Here’s a step-by-step solution:

### Step 1: Understand the Problem
The half-life of carbon-14 is given as 5730 years. The artifact has 80% of the original carbon-14 remaining. We need to find out how long ago the tree (from which the wood was taken) died.

### Step 2: Use the First-Order Kinetics Equation
The decay of carbon-14 follows first-order kinetics, described by the equation:

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