standard_description: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
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.


aligns: no