options: Define, evaluate, and compare functions.

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

Use functions to model relationships between quantities.

Model periodic phenomena with trigonometric functions.

Understand the concept of a function and use function notation.

Construct and compare linear and exponential models and solve problems.

Extend the domain of trigonometric functions using the unit circle.

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

Prove and apply trigonometric identities.

Build new functions from existing functions.

Analyze functions using different representations.

Build a function that models a relationship between two quantities.
problem_activity: Task
According to Wikipedia, the International Basketball Federation (FIBA) requires that a basketball bounce to a height of 1300 mm when dropped from a height of 1800 mm.
Suppose you drop a basketball and the ratio of each rebound height to the previous rebound height is 1300:1800. Let $h$ be the function that assigns to $n$ the rebound height of the ball (in mm) on the $n^{\rm th}$ bounce. Complete the chart below, rounding to the nearest mm.
{"table": [{"_attributes": {"class": ["centered", "narrow"]}, "tbody": [{"tr": [{"th": [{"_value": "$n$"}, {"_value": "$h(n)$"}]}, {"td": [{"_value": "0"}, {"_value": "1800"}]}, {"td": [{"_value": "1"}, {}]}, {"td": [{"_value": "2"}, {}]}, {"td": [{"_value": "3"}, {}]}]}]}]}
Write an expression for $h(n)$.
Solve an equation to determine on which bounce the basketball will first have a height of less than 100 mm.


correct_option_index: 5