The mathematical law is that the rate of decay of C14 is proportional to the quanitity of C14. That is, C14' = -kC14.
Let t=0 be the year that the cotton for the shroud was harvested. Let "age" be the age of the shroud in 1989 when the analysis of the shroud was conducted. The facts that are given are these:
1. The amount of C14 in the shroud as measure by scientists in 1989 (C14(age)), was about 92% of the amount in living plants today.
2. The amount of C14 in living plants today is assumed to be the same as the amount of C14 in living plants when the shroud was made. (The shroud was made from plant material, thus, C14(age)= 0.92 times C14(0).
3. The function, C14(t), is a solution to C14' = -kC14, and so that function must be C14(t) = Ae^-kt, for some constant A.
4. A serviceable value for k is 0.0001245.
*During your calculations you'll be faced with an algebraic expression of the form p = e^qt, which you'll have to solve for t. That means getting t out of the exponent, and that means using ln.
The question is to find the age of the Shroud of Turin as well as to find the half-life of Carbon 14 (aka C14).
I'm at a loss as to how I should go about solving this, so please, any help will be much appreciated!