Carbon-14 has a half-life of 5,730 years. If scientists discover a mummified Cro-Magnon specimen, they will first want to determine its age. When examining a sample from the bone remains, the scientists discover the specimen is composed of 25% carbon-14 and 75% nitrogen-14. How old is this specimen?

the specimen has 11460 years old

Explanation:

if the live sample has as initial amount of Yo C14, the dead sample will have 0.25Yo of C14.

the rate of decay of radiactive matter over time is

Y (t) = Yo * e (( - t * Ln2) / T)

∴ Y (t) = 0.25Yo; T = 5730

⇒ 0.25Yo = Yo * e (( - t * Ln2) / 5730)

⇒ 0.25 = e (( - t * Ln2) / 5730)

⇒ Ln (0.25) = ( - t * Ln2) / 5730

⇒ - 7943.466 = - t * Ln2

⇒ 7943.466 / Ln2 = t

⇒ t = 11460 year