The half life for C14 is 5730 years.
We assume that Carbon 14/ Carbon 12 ratio was steady for living organisms over time, the problem is actually telling us that
[tex] \frac{Nt}{N0} [/tex] = 0.0725 = [tex] \frac{1}{2} [/tex]ˣ
Take the natural logarithm and In on both sides.
ln(0.725) = ln[tex] \frac{1}{2} [/tex]ˣ
= - 0.3216 = xln ([tex] \frac{1}{2} [/tex] = -0.6931x.
So x = (-.3216) / (-0.6931) = 0.464
or
t/t₁/₂ = 0.464
So t = 0.464 x t₁/₂ = 0.464 * 5730 yrs = 2660 years.
