carbon 14 is used for carbon dating.

Question

Carbon 14 is used for carbon dating. Carbon 14 decays at a rate of y=Y_oe^{-(ln2)(1/5700)t}. If a mummy is found and has exactly 1/3 of its carbon 14 remaining, how long has the mummy been entombed.

Answer 1

Y₀/3 = Y₀e^{-ln2(1/5700)t}

Y₀/3 = Y₀e^-0.00012t

1/3 = e^-0.00012t

ln(1/3) = ln e^-0.00012t

-1.09862 ≈ -0.00012t

9155.18 ≈ t