Question

a. Make a scatter plot of the data in the table below.
b. Does it appear that a linear model or an exponential model is the better fit for the​ data?
                                                                                             
x
1
2
3
4
5
6
y
9.8
13.7
19.2
26.9
37.6
52.7
Question content area bottom
Part 1
a. Choose the scatter plot below.
A.
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A scatterplot has a horizontal x-axis labeled from 0 to 55 in increments of 5 and a vertical y-axis labeled from 0 to 55 in increments of 5. Points are plotted at (9.8, 9.8), (13.7, 13.7), (19.2, 19.2), (26.9, 26.9), (37.6, 37.6), and (52.7, 52.7). All coordinates are approximate.
B.
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A scatterplot has a horizontal x-axis labeled from 0 to 55 in increments of 5 and a vertical y-axis labeled from 0 to 6 in increments of 1. Points are plotted at (9.8, 1), (13.7, 2), (19.2, 3), (26.9, 4), (37.6, 5), and (52.7, 6). All coordinates are approximate.
C.
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Answer 1

To analyze the data you provided and generate a scatter plot, let’s summarize the steps required for both parts of your question.

### Part 1: Scatter Plot

The data from your table is as follows:

| x | y |
|---|------|
| 1 | 9.8 |
| 2 | 13.7 |
| 3 | 19.2 |
| 4 | 26.9 |
| 5 | 37.6 |
| 6 | 52.7 |

The scatter plot should depict the relationship between the values of x and y.

### Choosing the Correct Scatter Plot from Options:
1. **Option A:**
- Contains points (9.8, 9.8), (13.7, 13.7), etc.
- This is incorrect because the y-values and x-values are not paired correctly.

2. **Option B:**
- Contains points such as (9.8, 1), (13.7, 2), etc.
- This is incorrect since it does not reflect the correct y-values for each x-value.

3. **Option C:**
- This option does not provide data points but appears to indicate it will plot them correctly as labeled.
- Without specific points displayed, it's hard to verify, but it might be the best representation if it actually uses the correct coordinates.

Since I can't physically plot the graph here, use the data points above to plot (x, y) pairs as follows:
- (1, 9.8)
- (2, 13.7)
- (3, 19.2)
- (4, 26.9)
- (5, 37.6)
- (6, 52.7)

### Part 2: Model Fit Evaluation

To determine if a linear or exponential model fits better, we look at the trend in the points:

- **Linear Model:** Represents a constant rate of change. If the increase in y-values is approximately the same for equal increments in x, a linear model is appropriate.
- **Exponential Model:** Characterizes growth that increases at a percentage. If the y-values increase increasingly larger amounts as x increases (not constant), an exponential model is likely a better fit.

#### Analysis of the Given Data:
- The differences between the y-values are not constant:
- From y(1) to y(2): 13.7 - 9.8 = 3.9
- From y(2) to y(3): 19.2 - 13.7 = 5.5
- From y(3) to y(4): 26.9 - 19.2 = 7.7
- From y(4) to y(5): 37.6 - 26.9 = 10.7
- From y(5) to y(6): 52.7 - 37.6 = 15.1
- The increasing differences indicate an exponential growth pattern, since the increase in y becomes progressively larger as x increases.

### Conclusion:
1. The correct scatter plot would show the points (1, 9.8), (2, 13.7), (3, 19.2), (4, 26.9), (5, 37.6), (6, 52.7).
2. The data appears to fit an **exponential model** better than a linear model based on the increasing differences between y-values.