Dr. Hovind (R6): The shape of the curve of the line is based on too few real measurements to be reliable.
It’s not clear to me what Dr. Hovind is talking about. If he is referring to the carbon-14 decay curve then he has demonstrated, once again, his ignorance of radiometric dating.
The decay curve is mathematically based on the fact that every atom of carbon-14 in a sample has the same chance of decaying during each second of time, that being predicted by quantum mechanics, one of the most successful of the modern scientific revolutions.
The random character of radioactive decay is a special case of the indeterminacy of quantum theory, as was pointed out in 1928 by George Gamow, Ronald Gurney and Edward Condon. They showed that a particle held inside the nucleus by a "potential barrier" may be able to "tunnel through" the barrier and emerge on the other side, since if the barrier is finite the wave function of the particle is not completely localized and there is a finite probability that the particle will be outside the nucleus.
Since we are dealing with millions of C-14 atoms in even the smallest samples, the amount of C-14 remaining with respect to time will be an excellent approximation of an exponential decay curve. Statistics assure us of that. Indeed, it would be absurd to speak of the half-life of a radioactive isotope if it did not have an exponential decay curve!
Once we have a good approximation of the halflife for carbon-14, its decay curve can be constructed with complete confidence. We don’t need Egyptian mummies or what have you at that point. At that point it’s just a routine exercise in math. If you want additional assurance that we have the correct halflife, then look at the close correlation between C-14 dates and tree ring dates (after correcting for variances in C-14 production caused by changes in the earth’s magnetic field). The snug fit indicates that the halflife of C-14 is stable and accurately known. Therefore, so is its decay curve.
Today, the half-lives of those radioactive elements used in dating are known to a few percent by careful laboratory study. So, there’s no problem in getting an accurate decay curve.