Question

Which of the following correctly graphs the geometric sequence?

n f(n)
0 11
1 16.5
2 24.75
3 37.125
4 55.6875
(1 point)
Responses

[Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 6 in increments of 1 and the y-axis ranges from 0 to 6000 in increments of 1000.
[ Image with alt text: Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 6 in increments of 1 and the y-axis ranges from 0 to 6000 in increments of 1000.

Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 60 in increments of 10 and the y-axis ranges from 0 to 6 in increments of 1.
Image with alt text: Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 60 in increments of 10 and the y-axis ranges from 0 to 6 in increments of 1.

Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 6 in unit increments and the y-axis ranges from 0 to 60 in increments of 10.
Image with alt text: Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 6 in unit increments and the y-axis ranges from 0 to 60 in increments of 10.

Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 10 in increments of 1 and the y-axis ranges from 0 to 60 in increments of 10.
Image with alt text: Five points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 10 in increments of 1 and the y-axis ranges from 0 to 60 in increments of 10.
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Answer 1

To determine which graph correctly represents the given geometric sequence, we first analyze the provided values:

- \( f(0) = 11 \)
- \( f(1) = 16.5 \)
- \( f(2) = 24.75 \)
- \( f(3) = 37.125 \)
- \( f(4) = 55.6875 \)

Next, we need to identify the pattern in the geometric sequence. A geometric sequence has a common ratio \( r \), which can be calculated as follows:

- \( r = \frac{f(1)}{f(0)} = \frac{16.5}{11} = 1.5 \)
- \( r = \frac{f(2)}{f(1)} = \frac{24.75}{16.5} = 1.5 \)
- \( r = \frac{f(3)}{f(2)} = \frac{37.125}{24.75} = 1.5 \)
- \( r = \frac{f(4)}{f(3)} = \frac{55.6875}{37.125} = 1.5 \)

Now, we observe that the common ratio \( r = 1.5 \). Thus, the points increase exponentially as \( n \) increases.

Now we can check the values to find the appropriate range for the x-axis and y-axis for the graphs:

- For \( n = 0 \) to \( n = 4 \), the x-axis should range from \( 0 \) to \( 4 \).
- The corresponding y-values are:
- At \( n = 0 \), \( y = 11 \)
- At \( n = 1 \), \( y = 16.5 \)
- At \( n = 2 \), \( y = 24.75 \)
- At \( n = 3 \), \( y = 37.125 \)
- At \( n = 4 \), \( y = 55.6875 \)

Thus, the y-range should be from \( 0 \) to at least \( 60 \).

Given these observations, we want to find the graph that matches the requirements of having the x-axis from \( 0 \) to \( 4 \) and y-axis up to at least \( 60 \).

None of the options you provided contain exact numbers matching from `0` to `4` and `0 to 60`, but we are searching for the correct trend of increasing y-values that correlate sensibly with the x-values provided.

Choose the graph that displays the characteristics of an exponential increase from these coordinates. If one of the graphs indicates a range that includes (0, 11), (1, 16.5), (2, 24.75), (3, 37.125), and (4, 55.6875), with the proper x and y scaling, then that would be the correct graph to represent the geometric sequence.

If you have specific descriptions of the graphs or images referenced, please share those details for a more thorough evaluation.