I need a rational function/equation beyond the contrived d=rt and work problems typically given in beginner algebra.
I am teaching such a class and would like to motivate the study of techniques for solving rational equations by a legitimate example. Wikipedia lists the following applications:
(i) fields and forces in physics, (ii) spectroscopy in analytical chemistry, (iii) enzyme >kinetics in biochemistry, (iv) electronic circuitry, (v) aerodynamics, (vi) medicine >concentrations in vivo, (vii) wave functions for atoms and molecules, (viii) optics and >photography to improve image resolution, and (ix) acoustics and sound
In particular, I think the enzyme kinetics, medicine concentration, and acoustic/sound applications might be most accessible, but am having difficulty finding actual calculations. Can you please provide an example and/or a resource?
Thank you for taking the time to reply, Dan. I found a satisfactory solution along the lines of your second response.
A "real world" application of rational functions is the "Thin Lens Equation" which relates focal length, object distance, and real image distance. It is as practical as it gets. Cameras, eyeballs, magnifying glasses, etc all operate using this principle in some capacity. The derivation of it is straight forward and only uses similar triangles. Furthermore, the magnification measure (when the object does not rest at 2F) is a proportion.
I won't be implementing it in my lesson, but it might be possible to create an exploration into calculating an object's height from a photograph. There are potential complications with this, as in the photo may be a model and the picture an optical illusion. This might be overcome by analyzing a second photograph. I haven't thought this aspect through as I don't have time right now. But it seems worth sharing should any teacher come across this thread in the future.