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 f(x) = 54 f(x) = (54)x f(x) = (54)x – 1

Answer 1

54, 36, 24 are the 1st 3 element of a geometric progression with 2/3 as a common ratio: PROOF:
the 1st term is 54, (a₁= 54) the 2nd term a₂ = 24, then
(a₂ = a₁.r) or 36 = 54.r → r= 36/54 = 2/3. Same logique for the 3rd term. 
So 2/3 is common ratio. We know that :U(n) = a.(r)ⁿ⁻¹. Then if a =54 and r = x (given by the problem), then f(x) = 54.xⁿ⁻¹
n, being the rank of any element of this geometric progression

Answer 2

The answer is B on e2020