The spectrum of high Tc superconductors as studied by local tunneling spectroscopy, presents many unique conceptual challenges. These spectra display a wide range of behavior, often times varying over the sub-nanometer length scale. We have come to the point where we need a method of categorizing the spectra in order to reveal the underlying physical processes. This must be undertaken with caution, for it is easy to parameterize a series of curves arbitrarily. The parameterization process has to be undertaken with a minimalistic attitude. This is what I have endeavored to present here. Here we have an evolution in the understanding and parameterization of the Local Density of States of the High Tc superconductor Bi2Sr2CaCu2O0+? (Bi-2212). We start with the concept of a d-wave BCS model, to which we add a simple extension in the modeling of the lifetimes, in order to deal with our measured spectra. This model proves highly successful across a wide range of hole densities (dopings), and allows us to track quasiparticle lifetime changes as they evolve with doping. However our first model has some short comings, especially at low dopings where a ?kink? phenomenon manifests itself. It also fails to reproduce the Quasiparticle Interference Patterns (QPI) in q-space. It is here we introduce the second more complex model, that capture both real and k-space phenomena. This represents an effective description of the electronic properties of the cuprates through their whole range of dopings. From this effective theory we are able to predict the bulk thermodynamic and electronic properties and trends of our samples. This can be accomplished at first for individual representative data, and has the possible to be extended from one spectrum to N, although we suffer from lack of computational power, as well as the increased complexity of our fits. These I feel will be overcome in the future, as we gain a better understanding of the relationships and the meaning of our fits. Our effective model represents the first step on the road to understanding the processes at work in high Tc superconductors.