Radioactive nuclei decay randomly — no one can predict when any individual nucleus will decay. Yet the aggregate is perfectly predictable: after each half-life, exactly half remain. N(t) = N₀·2^(−t/T½). Decay probability per nucleus in dt: p = 1−2^(−dt/T½). C-14 half-life 5730 years (dates organic material to ~50,000 years). U-238 half-life 4.47 billion years (dates rocks). The simulator shows real statistical fluctuations around the theoretical curve.
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