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

general formula:

f(x) = ab^(x-1)

where a is the initial value, b is the common ratio, and x is the independent variable (here, the # of bounces)

the initial value is simply the height of the first bounce (54)

to find the common ratio, simply take any height and divide by the previous height
(ex: 36/54, 24/36)

once you have your a and b value, plug them back into the equation. your result should match one of the choices.