We have 71%, so what I can do is just say .71 times our original amount.
If you have and I have 2/3 of the amount of money you have, you take 2/3 times 5.
Similarly, in a population which grows exponentially with time there is the concept of "doubling time".
We started the first article by talking about carbon dating and the Dead Sea scrolls.
Exactly the same treatment can be applied to radioactive decay.
However, now the "thin slice" is an interval of time, and the dependent variable is the number of radioactive atoms present, N(t). If we have a sample of atoms, and we consider a time interval short enough that the population of atoms hasn't changed significantly through decay, then the proportion of atoms decaying in our short time interval will be proportional to the length of the interval.
We end up with a solution known as the "Law of Radioactive Decay", which mathematically is merely the same solution that we saw in the case of light attenuation.
We get an expression for the number of atoms remaining, N, as a proportion of the number of atoms N, where the quantity l, known as the "radioactive decay constant", depends on the particular radioactive substance.
Let's look further at the technique behind the work that led to Libby being awarded a Nobel prize in 1960.
Carbon 14 (C-14) is a radioactive element that is found naturally, and a living organism will absorb C-14 and maintain a certain level of it in the body.
This question can be answered using a little bit of calculus. Once we have an expression for t, a "definite integral" will give us the mean value of t (this is how "mean value" is defined).
From the equation above, taking logarithms of both sides we see that lt = -ln(N/N.
The steps are the same as in the case of photon survival.