Question

A bouncing ball reaches a height of 54 inches at its first peak, 36 inches at its second peak, and 24 inches at its third peak. Which formula represents this scenario?

f(x) = 54(two-thirds) Superscript x
f(x) = 54(two-thirds) Superscript x minus 1
f(x) = Two-thirds(54)x
f(x) = Two-thirds(54)x – 1

Answer 1

Answer: B

Explanation:

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Answer 2

f(x) = 54(two-thirds) Superscript x minus 1

Explanation:

Given that:

First peak : 36 / 54=2/3

Second peak : 24 / 36 = 2/3

The common ratio here is 2/3 ; which mean each bounce height is 2/3 of previous height

Modeling this using geometric progression :

An=a1r^(n-1)

An = nth term of a geometric progression

a1=first term

r=common ratio = 2/3

n = nth term

a1=54

Substituting into the above formular :

An=54(2/3)^(n-1)