Which sequence is modeled by the graph below? points: (2,8) (3,4) (4,2) (5,1)
a. an = one half (16)n − 1
b. an = 4(2)n − 1
c. an = 16(−2)n − 1
d. an = 16( one half )n − 1

Step-by-step explanation:

This sequence is geometric because while x is going up by 1, the y sequence has a common ratio.

That is, term/previous equals same number per consecutive y terms.

So 1/2=2/4=4/8 is the common ratio.

The first term is when x=1. We can find this y by figuring out what we can multiply to our common ratio, 1/2, to get the next term,8.

Since 8(2)=16, then the first term is 16.

In general,

Or if preferred:

where is first term and is common ratio.

Plug in information:

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).

answer: 0.1,0.85

step-by-step explanation: