A radioactive sample has a half-life of 3 years. What fraction remains after 9 years?

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Multiple Choice

A radioactive sample has a half-life of 3 years. What fraction remains after 9 years?

Explanation:
The idea tested is how a half-life reduces the amount of a radioactive sample over time. Each half-life cuts what you have in half. Since the half-life is 3 years, after 9 years you’ve gone through 9 ÷ 3 = 3 half-lives. Halving three times gives: (1/2) × (1/2) × (1/2) = 1/8. So the remaining fraction is 1/8 (which is 12.5%).

The idea tested is how a half-life reduces the amount of a radioactive sample over time. Each half-life cuts what you have in half. Since the half-life is 3 years, after 9 years you’ve gone through 9 ÷ 3 = 3 half-lives. Halving three times gives: (1/2) × (1/2) × (1/2) = 1/8. So the remaining fraction is 1/8 (which is 12.5%).

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