# Carbon dating exponential

When a plant or animal is alive it continually replenishes the carbon in its system. When it dies the carbon it contains no longer replenishes, hence the \(^C\) begins to decay.It is a chemical fact that the rate of decay is proportional to the amount of \(^C\) in the body at that time.Asked by: William Baker Carbon 14 (C14) is an isotope of carbon with 8 neutrons instead of the more common 6 neutrons.

\] After 5730 years, there is \[ 1/2 C \] carbon 14 remaining. \] Taking \(\ln\) of both sides and dividing by 5730 gives \[ k = \dfrac = -0.000121.\] Now we use the fact that there is 9% remaining today to give \[ 0.09 C = Ce^.

We have devices to measure the radioactivity of a sample, and the ratio described above translates into a rate of 15.6 decays/min per gram of carbon in a living sample.

And if you play with the exponential decay equations, you can come up with the nice formula (1/2)=(current decay rate)/(initial decay rate), where n is the number of half lives that have passed.

Voila, now you can tell how old a sample of organic matter is.

Some notes: 1) Obviously, this technique only works for dead organic material.