Click for printer friendely version of this HowTo Algebraic Models Some processes are so simple that they can be described in terms of algebraic equations, either explicitly, or implicitly as the solution to a differential equation. Algebraic equations are usually defined by applying some law of physics like conservation of mass or conservation of momentum or a time or space dependent equation describing the temporal movement of something. For example this is an explicit algebraic model: $$\textrm{age} = x - \textrm{date of birth},$$ where $x$ is today's date. An example of an implicit algebraic equation is the description of the time course of binding of drug to a receptor. The dynamics is best characterized by a differential equation (equating changes in the fraction of bound receptors to the difference between rates of forming and unforming bound receptors) which has a simple algebraic solution: $$b = 1 - e^{-(kD + l)t},$$ where $b$ is the fraction of bound receptors, $kD$ is the rate of making bound receptors, $l$ is the rate of unmaking bound receptors and $t$ is time. Algebraic models are usually easy to explore because we can simple generate a sequence of values for the independent variable and plot the resulting values of the model's dependent variable. Click for printer friendely version of this HowTo

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