Question

Geometric Sequences Quick Check
1 of 51 of 5 Items
Question
Which of the following correctly graphs the geometric sequence?

This table shows the relationship between input values (n) and the corresponding output values for the function f(n) showing the values rising by a factor of 1.5 each time, suggesting an exponential function.
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 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 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 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.
Skip to navigation

Answer 1

To determine which graph correctly represents the geometric sequence described, we first need to calculate the outputs (f(n)) for the given inputs (n) and confirm they match the values provided. The growth factor of the sequence is 1.5, beginning at 11.

Here's how the output values are calculated:

1. **n = 0**:
\( f(0) = 11 \)

2. **n = 1**:
\( f(1) = 11 \times 1.5 = 16.5 \)

3. **n = 2**:
\( f(2) = 16.5 \times 1.5 = 24.75 \)

4. **n = 3**:
\( f(3) = 24.75 \times 1.5 = 37.125 \)

5. **n = 4**:
\( f(4) = 37.125 \times 1.5 \approx 55.6875 \)

Therefore, the points plotted would be:
- (0, 11)
- (1, 16.5)
- (2, 24.75)
- (3, 37.125)
- (4, 55.6875)

Now we analyze the given options to find the one that accurately reflects these points.

1. **First image**: x-axis from 0 to 6 and y-axis from 0 to 60 — might work because it captures the output values.
2. **Second image**: x-axis from 0 to 6 and y-axis from 0 to 6000 — not correct, as the y-values exceed this range.
3. **Third image**: x-axis from 0 to 60 and y-axis from 0 to 6 — the axes are reversed, and the y-values are not represented correctly.
4. **Fourth image**: x-axis from 0 to 10 and y-axis from 0 to 60 — y-axis is still not sufficient for accurate representation.

The **first image** is the most likely candidate, as it appropriately places the given output values within the range of the y-axis, accommodating the values correctly from your data table.

Choose the **first option** as the correct graph for the geometric sequence provided.