Question

On a coordinate plane, 3 points are plotted. The points are (1, 80), (2, 20), (3, 5). Which function can be used to represent the graphed geometric sequence? f(x) = 80(One-fourth) Superscript x minus 1 f(x) = 320(One-fourth) Superscript x minus 1 f(x) = 80(4)x – 1 f(x) = 320(4)x – 1

Answer 1

(A)
`f(x)=80\left((1)/(4)\right)^(x-1)`

Explanation:

Given the three points plotted on a coordinate plane

• (1, 80)
• (2, 20)
• (3, 5)

Let us consider the values in the y-axis i.e. f(x)

80, 20, 5

We notice that each succeeding term occurs by the division of the previous term by 4.

Precisely:

`(80)/(4) =20\\(20)/(4) =5`

This is a geometric sequence where the:

First Term =80

Common ratio =
`(1)/(4)`

Therefore, the function which can be used to graph the geometric sequence is:

`f(x)=80\left((1)/(4)\right)^(x-1)`