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?

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    $\begingroup$ matheducators.stackexchange.com ? $\endgroup$ Aug 16, 2014 at 23:41
  • $\begingroup$ I would stick to the "contrived" examples in textbooks. They work and require only a minimum of explanation. My guess is that you would spend too much time explaining any "real life" applications, which are rarely simple, only to confuse the matter. Your students and supervisor probably won't appreciate all the trouble you went to... "Why are you teaching wave mechanics in an elementary algebra class, Mr. Mtn?" Or biochemistry, or aerodynamics, etc. $\endgroup$ Aug 17, 2014 at 3:52
  • $\begingroup$ Sorry if that sounds a little negative. You might use applications from other courses they are currently taking or have taken, e.g. physics or economics -- something already familiar to them. $\endgroup$ Aug 17, 2014 at 14:54
  • $\begingroup$ Even then, there is some risk that students may not have thoroughly mastered the material from other courses. If you insist on drawing on other applications, pay very close attention the students' reaction to your presentation. If they seem puzzled or overly restless, cut it short and present a more textbookish example. Even if things go well, you probably shouldn't test them on mastery of this outside material. $\endgroup$ Aug 18, 2014 at 13:03

1 Answer 1


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.


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