# Exponential and logarithmic functions in carbon 14 dating

However, I note that there is no beginning or ending amount given.How am I supposed to figure out what the decay constant is?I can do this by working from the definition of "half-life": in the given amount of time (in this case, hours.

The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon-12, denoted 12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope).The ratio of the amount of 14C to the amount of 12C is essentially constant (approximately 1/10,000).When an organism dies, the amount of 12C present remains unchanged, but the 14C decays at a rate proportional to the amount present with a half-life of approximately 5700 years.This change in the amount of 14C relative to the amount of 12C makes it possible to estimate the time at which the organism lived.

A fossil found in an archaeological dig was found to contain 20% of the original amount of 14C. I do not get the $-0.693$ value, but perhaps my answer will help anyway.

If we assume Carbon-14 decays continuously, then $$C(t) = C_0e^,$$ where $C_0$ is the initial size of the sample. Since it takes 5,700 years for a sample to decay to half its size, we know $$\frac C_0 = C_0e^,$$ which means $$\frac = e^,$$ so the value of $C_0$ is irrelevant.

## Exponential and logarithmic functions in carbon 14 dating comments

• Exponentials & Logarithms - Cool math Algebra Help Lessons.

## paulette60

You've got this stuff in you called Carbon-14. It comes from cosmic rays that rain down on the earth and us from outer space. By the way, you are mostly Carbon-12, which is not radioactive. That's why we are called "Carbon-based life forms." Man, I've really watched too much Star Trek. Scientists use Carbon-14 to make.…