You may want to study some basics in multivariate math, say the first several Chapters of Morse and Feshbach to understand my expressions of exponential functionals. You might also complement your expressions with a Little, Brown Handbook.
Um, okay.
Anyone who has actually studied physics to the level of being familiar with the concepts of theoretical physics would know that exponential/logarithmic functions are quite simple and basic math which do not involve multivariate analysis. This is high school level math.
Also, anyone who is knowledgeable about theoretical physics knows that the rate of radioactive decay is invariable.
FYI, the reason I keep lumping exponents together with logarithms is that they are inverse functions--like multiplication is the inverse function of division.
Let me help you out a little: radioactive decay is described by the equation,
A=A0e-(kt/T1/2),
where A is the current quantity of the material,
A0 is the starting quantity of the material,
e is the "natural number", which has a value of ~2.71,
k is the decay constant which is ~0.693,
t is the elapsed time of decay (time since quantity A0 existed), and
T1/2 is the half-life of the material.
(The reason I put the tilde on those numbers is because they are truncated after 3 significant digits. They are like pi, in that they have an infinite number of digits after the decimal point.) In order to measure how old a sample is, all you need to do is to measure the quantities of the radioisotope and its decay products. From that, you can determine the starting quantity. (There are other ways to determine starting quantity, as well.) After that, it is just a matter of solving for t and plugging in numbers to determine how old the substance is. The technique is only inaccurate at the extremes: at the beginning, when too little time has elapsed to observe any radioactive decay, and at the end when there is too little radioisotope left to measure. In between those extremes, the technique is quite precise.
BTW, the mathematical formula used to calculate radioactive decay is the same formula used to calculate compound interest on your savings account. Have you ever seen the interest earned on your account jump around the way Answers In Genesis claims elapsed time determined by radioisotope dating jumps around? I'd go so far as to say that if the amount of interest your account earns is drastically different from month to month, then either the balance has significantly changed, or the interest rate has changed.