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Actually the students shouldn't "encounter" the equation, they should
determine it from the lab. The Modeling approach has them graph the data,
and if it is a straight line, just find the equation. If it is not, then
they try different ways to make a modified graph by changing the X axis. If
they have X vs t and it "looks like a parabola" graph X vs t^2 and see if
they get a straight line. This is a fairly old fashioned approach. Of
course the students have to follow some rules for taking the data so that
the data is analyzable by this approach. If it is a 1/sqrt(x) relationship
they have to first make a graph of 1/x and then by noticing the curvature
try 1/sqrt(x). So for most situations all they need is to recognize is
linear, inverse, square, and square root relationships.