You can use the formula for getting the xth term of a geometric sequence for the graphed points.
The function that represents the graphed geometric sequence is given by
Option A: [tex]f(x) = 80 \times (\dfrac{1}{4})^{x-1}[/tex]
There are three parameters which differentiate between which geometric sequence we're taking about.
Suppose the initial term of a geometric sequence is [tex]a[/tex] and the term by which we multiply the previous term to get the next term is [tex]r[/tex]
Then the sequence would look like
[tex]a, ar, ar^2 , ar^3 ....[/tex]
(till the terms to which it is defined)
Thus, the xth term of such sequence would be
[tex]f(x) = \text{xth term} = ar^{x-1}[/tex]
The points plotted in the graph are
(1,80), (2, 20), (3, 5)
The x coordinate shows the position of the term and the y coordinate shows the value of that position's term in the sequence.
So we have the sequence as
[tex]80, 20, 5 ...[/tex]
Thus, a = 80
and we have
[tex]r = \dfrac{ar}{a} = \dfrac{20}{80} = \dfrac{1}{4}[/tex]
Thus, the multiplication factor for the given sequence is r = 1/4
Thus, by using the xth term formula, we have:
[tex]f(x) = \text{xth term} = ar^{x-1} = 80 \times (\dfrac{1}{4})^{x-1}\\\\f(x) = 80 \times (\dfrac{1}{4})^{x-1}[/tex]
Thus,
The function that represents the graphed geometric sequence is given by
Option A: [tex]f(x) = 80 \times (\dfrac{1}{4})^{x-1}[/tex]
Learn more about geometric sequence here:
https://brainly.com/question/11266123
Answer:
The answer is Option A
Step-by-step explanation:
I hope this helps with you situation
