options: Understand the concept of a function and use function notation.

Extend the domain of trigonometric functions using the unit circle.

Prove and apply trigonometric identities.

Define, evaluate, and compare functions.

Use functions to model relationships between quantities.

Build a function that models a relationship between two quantities.

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

Analyze functions using different representations.

Model periodic phenomena with trigonometric functions.

Build new functions from existing functions.

Construct and compare linear and exponential models and solve problems.

Interpret functions that arise in applications in terms of the context.
problem_activity: Task
On June 1, a fast growing species of algae is accidentally introduced into a lake in a city park. It starts to grow and cover the surface of the lake in such a way that the area covered by the algae doubles every day. If it continues to grow unabated, the lake will be totally covered and the fish in the lake will suffocate. At the rate it is growing, this will happen on June 30.
When will the lake be covered half-way?
On June 26, a pedestrian who walks by the lake every day warns that the lake will be completely covered soon. Her friend just laughs. Why might her friend be skeptical of the warning?
On June 29, a clean-up crew arrives at the lake and removes almost all of the algae. When they are done, only 1% of the surface is covered with algae. How well does this solve the problem of the algae in the lake?
Write an equation that represents the percentage of the surface area of the lake that is covered in algae as a function of time (in days) that passes since the algae was introduced into the lake if the cleanup crew does not come on June 29.


correct_option_index: 5