Modeling with Sinudoidal Functions - Foxes and Rabbits

Sinusoidal functions are a staple of Algebra 2 and Pre-Calculus but the modeling problems in the textbooks are always so dry. I can't stand any more weights on a spring or riders on a ferris wheel! I wanted to make a problem that would be more interesting than the classic textbook tropes and I also wanted students to experience data that could be modeled this way. Of course, data is never perfect so the data provided here can be modeled with sine or cosine but no model will completely exact. And that's the point!

Students will need to create a graph (the graph is provided but can be deleted before giving to students) and also comes with a set of 11 questions. Some of the questions are more mathematical (i.e., give a function that models the population) but some are more subject to interpretation (why do the fox and rabbit waves line up the way they do?). An answer key is included with general guidelines for answers though answers will vary between students (or groups).