options: Model periodic phenomena with trigonometric functions.

Use functions to model relationships between quantities.

Understand the concept of a function and use function notation.

Extend the domain of trigonometric functions using the unit circle.

Build new functions from existing functions.

Define, evaluate, and compare functions.

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

Analyze functions using different representations.

Construct and compare linear and exponential models and solve problems.

Prove and apply trigonometric identities.

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

Build a function that models a relationship between two quantities.
problem_activity: The estimated size for a population of rabbits and a population of coyotes in a desert habitat are shown in the table. The estimated population sizes were recorded as a part of a long-term study related to the effect of commercial development on native animal species.
|  Years since initial count (       *        n       *       )  |   0    |   3    |   6   |   9    |   12   |   15   |  18   |   21   |   24   |
|----------------------------------------------------------------|--------|--------|-------|--------|--------|--------|-------|--------|--------|
| Estimated number of rabbits (       *        r       *       ) | 14,989 | 10,055 | 5,002 | 10,033 | 15,002 | 10,204 | 4,999 | 10,002 | 14,985 |
| Estimated number of coyotes (       *        c       *       ) | 1,995  | 2,201  | 2,003 | 1,795  | 1,999  | 2,208  | 2,010 | 1,804  | 2,001  |
Below are sketches of each graph, with a curve fitted to the data.
[IMG]
[IMG]
Write the function for each situation and then calculate the two different numbers of years where the population estimate is about 13,000 for rabbits and 2,100 for coyotes.


correct_option_index: 0