Use these with caution. Know your audience!
1. Three parameters define a constant and a single exponential. If we take the constant to represent production of erythrocytes and let the exponential account for red cell lysis and degradation, we are forced to neglect the rest of the elephant. You do this at your peril.
2. Three parameters can indeed fit an elephant if there are no constraints placed on the fit. If you are willing to accept an unbounded sum of squares of the errors, a circle with a line segment crossing its circumference at about 10:00 o'clock or an upside-down letter Q looks a lot like an elephant.
3. Having wrestled for years with the problem of fitting an elephant, I can say with some certainty that at least 43 parameters and 29 compartments are required to give even a rough approximation to an elephant.
4. Seriously, it is the power of constraints and simultaneous data fitting that permits the construction and testing of complex compartmental models. Modelers and kineticists often find it extremely difficult to discover even one model that accounts for a series of complex, inter-related data sets. Parameters are introduced only as required by the data. This does not mean the model is correct (see How do you know your model is correct?), but it does mean that the hypothesis represented by the model is quantitatively consistent with the available data. This is a powerful assertion that is useful in making predictions and in experimental design.