Exponential decay, a paleontologist finds a bone that might be a dinosaur bone. in the laboratory she finds that the carbon-14 f
ound 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!
The half-life of Carbon-14 is 5760 years. <span>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.) </span> <span>The decay equation is y = ae^(-0.0856t) with t in days. </span> <span>To find the half-life, we solve for t such that y/a = 0.5. </span>
<span>0.5 = e^(-0.0856t) </span> <span>Take natural logs of both sides: </span> <span>-ln(2) = -0.0856t </span>
<span>-0.6931 = -0.0856t </span> <span>Divide both sides by -0.0856... </span> <span>8.096 = t </span>
