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In order to understand what the equations mean, firstly we define $\dot{V}$, the tumor cell population growth rate. Setting $V$ as the tumor cell population, we define:  \begin{equation}\dot{V}=\frac{dV}{dt}\end{equation}  It isn't necessary to use $\dot{V}$ instead of $\frac{dV}{dt}$, but is helpful when writing out the equations. Each variable in these equations has some effect on the tumor growth. One example is $\lambda$, the "intrinsic growth rate" of the tumor. Another is $a$, a placeholder for an exponent. Then $K$ is the "carrying capacity" of the tumor, and $b$ is shorthand for $\frac{1}{K}$, the inverse of the carrying capacity.  \\  Now that we know what the equations define, we can differentiate between them. \eqref{ExponentialFit} is the Exponential Fit Equation.  \subsection{Data Selection}  \subsection{Fitting Procedure}   After selecting the data, we fit each model to the data sets we gathered. For each of the seven models we tested, we gave each parameter the ability to change freely in a way so that the Sum of Squared Residuals was normalized and then minimized between the data and the curve. The normalization of the SSR values served the purpose of preventing the larger values at the end of data sets from being weighted more than those at the beginning. Without this normalization, many curves fit only to the initial and final points, while the data contained within these values were ignored by the minimization of the SSR function. The normalization applied an inverse square law to the SSR values so that the data contained in later values was reduced by a great amount and the data contained in early values was reduced by a small amount. The data as represented on our graphs was not normalized, only the SSR values that correspond to each point were.  
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