Radioactive Half-Life Decay Steps:

• Calculate number of half-lives: 36 years ÷ 12 years/half-life = 3 half-lives.
• Formula for remaining amount: initial mass × (1/2)^number of half-lives.
• Substitute values: 32 mg × (1/2)^3 = 32 mg × 1/8 = 4 mg.
• The sample decays to 4 mg of tritium after 36 years.

Why A is correct:

• After three half-lives, exactly 1/8 of the original radioactive material remains, per the half-life definition.

Why the others are wrong:

• B: Matches after two half-lives (24 years), not three.
• C: Subtracts one half-life incorrectly; no decay basis.
• D: Assumes no decay, ignoring half-life entirely.

Final answer: A