Question

The half-life of C14 is 5730 years. Living things have 1000 ppq C14. An animal bone has 125 ppq remaining - find the age without a decay curve.

Answer 1

Do you halve the half-life each time? As in:
5730 years = 500 ppq
2865 years = 250 ppq
1,432.5 years = 125 ppq?

Answer 2

No, and first off, lets consider what you're saying! After 5,700 years there would be 500 ppq but then you're also saying that after 1,400 years even less is remaining? That's not right, since as time goes on, the total amount of C14 decays!

Half-life is the amount of time it takes for half of your sample to decay. So for instance, after about 5,730 years you have 500 remaining. After another 5,730 years, your sample of 500 will decay to 250. Another 5,730 years and you'll end up at 125. So, 5,730*3=17,190 years.

To check your answer, you can check it against the function.
\[\ln(2)/t _{1/2}=k\]The rate, k, is just the natural log of 2 divided by the half-life.\[C _{14}(t)=C _{14}*e^{-kt}\]\[125=1000*e^{-1.21x10^{-4}t}\]\[\ln(125/1000)/-1.21*10^{-4}=t\]\[17190=t\]