Question

A bouncing toy reaches a height of 64 inches at its first peak, 48 inches at its second peak, and 36 inches at its third peak. which explicit function represents the geometric sequence of the heights of the toy? f(x) = 48 f(x) = 48 f(x) = 64 f(x) = 64

Answer 1

Below are supposed to be the correct choices, it can be found elsewhere:

f(x) = 48[5/6]x-1
f(x) = 48[3/4]x-1
f(x) = 64[3/4]x-1
f(x) = 64[5/6]x-1

The correct answer is f(x) = 64[3/4]x-1 as the geometric sequence general formula is: an=a1∙rn−1. I hope it helps.

Answer 2

`a_n= 64 * ((3)/(4))^(n-1)`

Explanation:

A bouncing toy reaches a height of 64 inches at its first peak.

A bouncing toy reaches a height of 48 inches at its second peak.

A bouncing toy reaches a height of 36 inches at its third peak.

So, the sequence becomes : 64, 48,36 ....

So, a = first term = 64

r = common ratio =
`(a_2)/(a_1) =(a_3)/(a_2)`

=
`(48)/(64) =(36)/(48)= (3)/(4)`

General explicit formula for G.P. =
`a_n= a r^(n-1)`

Substituting the values :

`a_n= 64 * ((3)/(4))^(n-1)`

Thus the explicit function represents the geometric sequence of the heights of the toy is
`a_n= 64 * ((3)/(4))^(n-1)`