Radioactive half-life decay

Steps:

• The bone has ¼ the original ¹⁴C, equivalent to (1/2)^n where n is the number of half-lives.
• ¼ = (1/2)^2, so n = 2 half-lives.
• Half-life is 5700 years.
• Age = 2 × 5700 = 11400 years.

Why B is correct:

• Two half-lives reduce the proportion to exactly ¼ by the exponential decay formula N = N₀(1/2)^t/T, where t/T = 2.

Why the others are wrong:

• A: One half-life gives ½ proportion, not ¼.
• C: Three half-lives give ⅛ proportion, too low.
• D: Four half-lives give 1/16 proportion, much too low.

Final answer: B