A team of biologists studied the relationship between the rabbit and wolf populations in a certain region. They note that the populations of the animals appear to vary periodically over time. Their observations are as follow:
a) For the wolves, a maximum population of 7,000 occurs 8 months into the study. A
minimum population of 3,000 occurs 12 months later.
b) For the rabbits, a minimum population 10,000 occurs 14 months into the study. The rabbit population was at its maximum of 40,000 two months after the study began.
- Write equations that model the rabbit population, r(t), and the wolf population, w(t), where t is months since the start of the study.
- Explain why you chose a sine or cosine model for each function.
- What are the average populations of rabbits and wolves? Justify your results.
- Graph each function, on the same set of axes, over the course of two years. Label all critical points.
- Explain the population trends, for each species, for each quarter of the cycle.
Identify the apparent cause of these trends.
Sample Solution
