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Lacey is standing on top of one of the tallest buildings in her town. She stands at the edge of the roof and drops a basketball. The ball falls 120 feet to the pavement below and begins bouncing. Each successive bounce is 20% shorter than the previous bounce. Which explicit formula describes this situation?

Lacey is standing on top of one of the tallest buildings in her town She stands at the edge of the roof and drops a basketball The ball falls 120 feet to the pa class=

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Solution

Given that the ball fall 120 feet

After that, Each successive bounce is 20% shorter than the previous bounce

The problem represents a geometric sequence

The first term is a = 120

common ratio is

[tex]r=120-(\frac{20}{100}\times120)=80[/tex]

There we would have formula to be

[tex]\begin{gathered} a_n=ar^{n-1} \\ \\ \Rightarrow a_n=120(80)^{n-1} \end{gathered}[/tex]

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