options: Build a function that models a relationship between two quantities.

Define, evaluate, and compare functions.

Model periodic phenomena with trigonometric functions.

Use functions to model relationships between quantities.

Interpret functions that arise in applications in terms of the context.

Construct and compare linear and exponential models and solve problems.

Interpret expressions for functions in terms of the situation they model.

Build new functions from existing functions.

Prove and apply trigonometric identities.

Understand the concept of a function and use function notation.

Extend the domain of trigonometric functions using the unit circle.

Analyze functions using different representations.
problem_activity: Task
Given below is a table that gives the populations of foxes and rabbits in a national park over a 12 month period. Note that each value of $t$ corresponds to the beginning of the month and $t = 0$ corresponds to the beginning of January.
|       $t$, month       |   |   |   |   |   |   |   |   |   |   |   |
|------------------------|---|---|---|---|---|---|---|---|---|---|---|
| $r$, number of rabbits |   |   |   |   |   |   |   |   |   |   |   |
|  $f$, number of foxes  |   |   |   |   |   |   |   |   |   |   |   |
Note that the number of rabbits and the number of foxes are both functions of time.
Explain why it is appropriate to model the number of rabbits and foxes as trigonometric functions of time.
Find an appropriate trigonometric function that models the number of rabbits, $r(t)$, as a function of time, $t$, in months.
Find an appropriate trigonometric function that models the number of foxes, $f(t)$, as a function of time, $t$, in months.
Graph both functions and give one possible explanation why one function seems to “chase” the other function.


correct_option_index: 2