ACT (Enhanced)MathematicsMedium
A paleontologist is dating a fossil using carbon-14. The amount of carbon-14 remaining in a sample can be modeled by the equation A(t) = A_0 * (1/2)^(t/5730), where A_0 is the initial amount and 5730 years is the half-life. If a fossil sample contains 12.5% of its original carbon-14, approximately how old is the fossil?
- A5,730 years
- B17,190 years
- C22,920 years
- D11,460 years
Show answer & explanationAnswer & explanation
Correct answer: B. 17,190 years
If 12.5% remains, this is equivalent to (1/2)^3, meaning 3 half-lives have passed. Multiply the number of half-lives by the half-life period to find the total age.
Why the other options are wrong
- A. Incorrect. This represents 50% of the original amount (1 half-life).
- C. Incorrect. This represents 6.25% of the original amount (4 half-lives).
- D. Incorrect. This represents 25% of the original amount (2 half-lives).
Half-Life Calculation
Half-life is the time required for a quantity to reduce to half its initial value. The remaining amount after 'n' half-lives is A_0 * (1/2)^n.
- Each half-life reduces the amount by 50%.
- The number of half-lives can be found by expressing the remaining percentage as a power of 1/2.
- Total age = (number of half-lives) * (half-life period).
Memory trick: Half-Life is 'Halving' over 'Time' to 'Decay'.