Carbon Dating Ancient Artifacts

Differential Equations · Axiom Academy

Carbon Dating Ancient Artifacts A scroll, a mummified body, a wooden tool — none of them come with a date stamped on. Radioactive decay gives archaeologists one anyway. Every living thing absorbs carbon-14 while it's alive, then stops the moment it dies — and from that instant, the C-14 already inside it decays on a fixed clock. Measure what's left, and the same differential equation that predicts radioactive decay hands you the age. How much C-14 is left — and how old does that make it? Drag the "percent remaining" slider to whatever a lab measurement reports, and watch the sample's decay curve place that reading in time. That's , solved backward for t . Same formula, three real discoveries Pick a specimen. Each one's lab-measured C-14 percentage plugs into the exact same — see how closely it lands on the age historians already know from other evidence. Beats 1 and 2 both leaned on one formula. Here's where it comes from — the same separable differential equation every radioactive decay obeys, solved once and then rearranged for the one thing archaeologists actually want: t . One decay equation, , is the whole method: measure the fraction of C-14 left, and hands back the age — no clock was ever running at the dig site, only atoms decaying at a fixed rate since the moment something died. Carbon-14's decay constant, fixed by its half-life Solved for time — the dating formula itself

This is the written version of the interactive lesson above. See the full Differential Equations course.