Question

Which sequence is modeled by the graph below? (6 points)

coordinate plane showing the points 2, 1; 3, 2; 4, 4; and 5, 8

Answer 1

This graph doesn't show a specific sequence. It is simply four points plotted on a coordinate plane. The x-coordinates of the points increase from left to right, but I can't infer a specific sequence from these points without additional information, man.

Answer 2

let
\[y=a(b)^x+c\]
x=2,y=1
\[1=ab^2+c ...(1)\]
x=3,y=2
\[2=ab^3+c ...(2)\]
x=4,y=4
\[4=ab^4+c ...(3)\]
x=5,y=8
\[8=ab^5+c ...(4)\]
(2)-(1),(3)-(2),(4)-(3) gives
\[1=ab^2(b-1) ...(5)\]
\[2=ab^3(b-1)...(6)\]
\[4=ab^4(b-1)...(7)\]
divide (6) by (5)
b=2


from (5)
1=4a
\[a=\frac{ 1 }{ 4 }\]
from (1)
\[1=\frac{ 1 }{4 }\times 4+c\]
c=0
hence
\[y=\frac{ 1 }{4 }2^x\]

Answer 3

or
\[y=2^{x-2}\]