enVision A|G|A offers a great resource for your high school math students. In this Algebra 1 project students analyze piecewise functions to model insect populations. Students learn about insect populations that have cyclical “booms” and “busts,” most notably the cicada, whose adult population booms every 17 years.
You will present the situation to the students by discussing why this population booms and busts, while other species’ populations are more stable. (In part, the next generation’s population depends on the environment’s carrying capacity and the species’ rate of reproduction.)