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advanced-mathA radioactive isotope decays so that 40% remains after 10 years. What is the approximate half-life?
A
About 7.5 years
B
5 years
C
10 years
D
4 years
Correct Answer: A
Choice A is the correct answer. Find half-life from remaining percentage.
- Model: where is half-life.
- Given: After 10 years, 40% remains: .
- Solve: Take log: .
- Calculate: years.
💡 Strategic Tip: Use logarithms or test values: if , then ✓.
Choice B is incorrect because after 10 years (2 half-lives), only 25% would remain. Choice C is incorrect because this would leave 50%, not 40%. Choice D is incorrect because this would leave about 18%.