The half-life of Carbon-14 is 5760 years.
For carbon-14 to have decayed down by a factor of 12, we know between 3 and 4 half-lives must have elapsed. Since 4 half-lives is only 23,000 years, the sample is considerably younger than a dinosaur bone. (Unless we assume it's been contaminated with modern carbon, in which case, any age calculation based on carbon-14 is worthless.)
The decay equation is y = ae^(-0.0856t) with t in days.
To find the half-life, we solve for t such that y/a = 0.5.
0.5 = e^(-0.0856t)
Take natural logs of both sides:
-ln(2) = -0.0856t
-0.6931 = -0.0856t
Divide both sides by -0.0856...
8.096 = t
The half-life is 8.096 days.
