ISSUES IN SOLUTION

Students need to plot the data first and roam through their function catalogue for possible fits. There is no physics of fit in this problem, i.e., no underlying physical model which would be THE one to apply based on first principles of physics, but rather there is a shape with parameters.

Students may try out several shapes plotted over the data, attempting various shapes, and in so doing altering the parameters. But eventually they should settle on a model equation or function and go after the parameters.

Several models may come up and students should be encourage to compare at all stages. Moreover, students may not be self-motivated to linearize the data, i.e., convert the model form to a linear relationship between converted variables the way scientists, e.g. chemists, routinely do. In the solution we offered the exponential model P = K e^(-a r) was considered first, but abandoned after the linearization process seemed to indicate the linearized data was not going to be linear.

The hyperbolic model seemed to work as a second choice and no other model was discussed. But we have had students offer other quite different models, e.g., K tan(a (1 - r/30)).
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