Question

Exponential decay, a paleontologist finds a bone that might be a dinosaur bone. in the laboratory she finds that the carbon-14 found in the bone is 1/12 of that found in living bone tissue. Could this bone have belonged to a dinosaur? Explain your reasoning. Hint- dinosaurs lived from 220 million years ago to 63 million years ago. Please show work!

Answer 1

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.