Question

A wooden boat discovered just south of the great pyramid in egypt has a carbon-14>carbon-12 ratio that is 72.5% of that found in living organisms. how old is the boat

Answer 1

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
$\frac{Nt}{N0}$ = 0.0725 = $\frac{1}{2}$ˣ

Take the natural logarithm and In on both sides.
ln(0.725) = ln$\frac{1}{2}$ˣ
= - 0.3216 = xln ($\frac{1}{2}$ = -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.