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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.
Some of the others are roughly contemporary with Christ.
We started the first article by talking about carbon dating and the Dead Sea scrolls.
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.
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.