14C: 12C ratio of the mummy is found to be 2/3 that of the scroll (2000 Yrs old). How old is the mummy?

Question

An Egyptian mummy is carbon-dated and compared with a scroll found in the Dead Sea, which is known to be 2000 years old. The 14C: 12C ratio of the mummy is found to be 2/3 that of the scroll. How old is the mummy?

Details and Assumptions:
* 14C is radioactive with a half-life of 6000 years (it decays into nitrogen). 12C is a stable isotope, so the amount of 12C in a sample remains constant over time.
* The ratio 14C:12C in an organism (plant or animal) at the time of its death is equal to the ratio of the isotopes in the air it breathed in. This ratio can be assumed to be constant over time.

Answer 1

3510 years older => 5510 years old
.
The ratio is x * y ^ (t / thl) where x is the original ratio, y is the decay value (0.5), t is the number of years ago and thl is the half-life time..
The mummy ratio is 2/3 the scroll ratio, so we can fill the equation to 2/3 = 0.5 ^ (t / 6000)
Rewrite into: t = ( log (2/3) / (log 0.5) ) * 6000
t = 3510.