The **half life of C** is about 5730 years, during which it (beta) decays into "N". In nature, about one atom in a million carbon atoms will be Carbon 14. A living organism constantly ingests carbon from its surrounding environment (and egests it back), so while alive **the ratio C/C** in the organisms remains at about the same as the surrounding environment 1/1,000,000. Once the organism dies, however, no new carbon in any form will be taken in.

Suppose that a sample of some dead organic matter is examined and is determined to have a **C/C ratio of 1/4,000,000**. About how long ago did this organism die?

First, I suspect you have not copied the problem exactly, as it should be talking not about "the half-life of C", but about "the half-life of

^{14}C", and not the "C/C ratio" but the

^{14}C/^{12}C ratio, or something similar. Details matter.

On the other hand, some details given here (such as the one-in-a-million claim) are not quite right, so this is a simplified version. And the calculation you need to do is far simpler than what you need in general, so I'm not going to refer you to a source on the topic, as I intended to.

Here's the question you need to ask yourselves: What fraction of the original Carbon-14 remains? How many times has it been halved?

EDIT: For the sake of clarity, the original

^{14}C/

^{12}C ratio was 1/1,000,000 (one in a million), and now it is 1/4,000,000. This is not as clear as it could be in the problem, especially if they really said "C/C", so I want to point it out to you.

If you need more help, please follow our guidelines by telling us something to help us know what she's learned so far, and what sort of help you need:

Welcome to our tutoring boards! :) This page summarizes some main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to...

www.freemathhelp.com