If the half-life of carbon-14 is 5700 years, and some plant remains from an archeological dig site have 1/8 the carbon-14 found in the atmosphere, what is the approximate age of the remains in the dig site in years?

- 700
- 5700
- 17000
- 45000

**Explanation**

The half-life is the time it takes for 1/2 of a radioactive substance to decay. For example, 20 units of a substance with a half-life of 5 years will have 10 units remaining after 5 years. In this example, carbon-14 has undergone 3 half-lives: 1 → ½; ½ → ¼; ¼ → 1/8.

3 x 5700 years = 17100 years.

- 700, incorrect, This answer results from multiplying the amount of sample by the half life, 5700/8.
- 5700, incorrect, This is the half-life, not the amount of time elapsed during three half-lives.
- 17000, correct.
- 45000, incorrect, This answer results from multiplying the half-life by the remaining fraction: 5700 x 8.

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