The question is a paleontologist discovers remains of animals that appear to have died at the onset of the Holocene ice age, between 10000 and 12000 years ago. what range of C^14 to C^12 ratio would the scientist expect to find in the animal remains?
Im not really sure how to go about solving this problem, any help would be apprecaited.
The exponential decay formula is given by:
$$m(t) = m_0 e^{-rt}$$
where $\displaystyle r = \frac{\ln 2}{h}$, $h$ = half-life of Carbon-14 = $5730$ years, $m_0$ is of the initial mass of the radioactive substance.
So, we have: $\displaystyle r = \frac{ln 2}{h} = \frac{\ln 2}{5730} = 0.000121$
The mass ratio of Carbon-14 to Carbon-12 is $\displaystyle m_0 = \frac{1}{10^{12}}$ (just look this up).
$12000$ years:
$\displaystyle m(12000) = m_0 e^{-rt} = 10^{-12}e^{-0.000121 \times 12000} \approx 2.34 \times 10^{-13}$
I think you can now do the $10,000$ year case (just change the value of $t$).
So, the scientist would find C14-to-C12 ratios ranging from:
$2.34 \times 10^{-13}$ - to - [insert $10000$ year calculation here].