Question

The values in the table represent an exponential function. What is the common ratio of the associated geometric sequence?
X | Y
1. | 9
2. | 36
3. | 144
4. | 576
5. | 2304

A. 9
B. 45
C. 4
D. 27

Answer 1

To find the common ratio of the associated geometric sequence based on the values provided in the table, we first need to find the ratio of consecutive \( Y \) values.

Given the values of \( Y \):

- \( Y_1 = 9 \)
- \( Y_2 = 36 \)
- \( Y_3 = 144 \)
- \( Y_4 = 576 \)
- \( Y_5 = 2304 \)

Now we can find the ratios:

1. Ratio from \( Y_1 \) to \( Y_2 \):
\[
\text{Ratio} = \frac{Y_2}{Y_1} = \frac{36}{9} = 4
\]

2. Ratio from \( Y_2 \) to \( Y_3 \):
\[
\text{Ratio} = \frac{Y_3}{Y_2} = \frac{144}{36} = 4
\]

3. Ratio from \( Y_3 \) to \( Y_4 \):
\[
\text{Ratio} = \frac{Y_4}{Y_3} = \frac{576}{144} = 4
\]

4. Ratio from \( Y_4 \) to \( Y_5 \):
\[
\text{Ratio} = \frac{Y_5}{Y_4} = \frac{2304}{576} = 4
\]

All of the ratios are equal to 4. Therefore, the common ratio of the associated geometric sequence is:

**C. 4**