What exactly did the decay rate formula do in The Amazing Spider-Man? What was it that was decaying?
According to the physicist who created the algorithm for the film, the "Decay Rate Formula" best describes the way in which cellular decay impacts on human mortality rates.
Clearly Curt Connors has a deep interest in cellular regeneration and hence would be most interested in the lifecycle of cells.
Being a physics professor who is also a fan of superhero comic books (I created a class at Minnesota titled: “Everything I Know About Physics I Learned from Reading Comic Books”) I recognize that one must invoke a "miracle exception from the laws of nature" in order to justify "spider-powers" or men mutated into giant lizards. When Andy Siegel asked me to create an equation that would relate to cell regeneration and human mortality — an equation called the "Decay Rate Algorithm" in the film — I nevertheless wanted to ground the formula in real science. Naturally, I thought of the Gompertz equation.
Armed with this background, I was ready to provide an equation to Andy Siegel, but I did not want to just simply send him the actual Gompertz equation, as there would seem to be little reason for the professional scientists in the film to not already know it. I therefore combined expressions from “The Reliability Theory of Aging and Longevity” by Leonid Gavrilov and Natalia Gavrilova into a single formula, and added extra terms (“mathematical glitter,” if you will) so that it would appear sufficiently complex. (The actual Gompertz equation can be written in a simple and compact manner that did not meet the visual needs of the filmmakers.)
You may also find the following video to be of interest. It's mostly about the (real world) application of the formula, but it does mention Spider-Man a few times
The decay rate algorithm is a series of continuous steps which has to do with successful animal regeneration, blood lines, and mortality in human capability. In which it is trying to en glace those capabilities in humans and in other animals, to make successful hybrids without there being any side affects such as a hosts taking over in the subject. One representative example of this concept from the film would be the lizard taking over Dr. Conner's subject. The reason the process was successful with Peter, and not the lizard experiment, is because the research done was his own blood, and the research could not continue without his blood line. That is why he left and why Peter was Spider man.