# Examples of exponential functions carbon dating

Here isotopes with longer half lives are used, which enables dating of geological formations and rocks. For example, in lava form, molten lead and Uranium-238 (standard isotope) are constantly mixed in a certain ratio of their natural abundance.Once solidified, the lead is "locked" in place and since the uranium decays to lead, the lead-to-uranium ratio increases with time.In the case of the Dead Sea scrolls, important questions required answers. Did they really date from around the time of Christ? Using Libby's radiocarbon dating technique, the scrolls have been dated, using the linen coverings the scrolls were wrapped in.One scroll, the Book of Isaiah, has been dated at 1917BC ±275 years, certainly long before the time of Christ.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.Again, we find a "chance" process being described by an exponential decay law.

The activity is measured at approximately 11.9 decays per minute.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.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.