Question

Use the graphing tool at the right to create a scatter plot for the data in the table. Use the shape of the scatter plot to determine if the data are best modeled by a linear​ function, an exponential​ function, a logarithmic​ function, or a quadratic function.
x
y
0
0
4
0.6
9
1.0
17
1.2
23
1.4
Part 2
Plot each​ point, one at a time. Using the graphing​ tool, start by plotting ​(0,0).
.
.
.
Question content area right
Part 1
-6
-3
3
6
9
12
15
18
21
24
27
-0.6
-0.3
0.3
0.6
0.9
1.2
1.5
1.8
x
y

Answer 1

To determine the best model for the data using the scatter plot, let's start by plotting the points one at a time based on the provided values. Here’s the data in table format for clarity:

| x | y |
|----|-------|
| 0 | 0 |
| 4 | 0.6 |
| 9 | 1.0 |
| 17 | 1.2 |
| 23 | 1.4 |

Now, let’s go through each point to visualize them. You can plot each of the following:

1. (0, 0)
2. (4, 0.6)
3. (9, 1.0)
4. (17, 1.2)
5. (23, 1.4)

### Plotting Points

1. Start with (0, 0) - This is the origin.
2. Next, plot (4, 0.6) - This point is slightly above the x-axis and to the right.
3. For (9, 1.0) - Plot this point further right and also slightly above the point (4, 0.6).
4. Plot (17, 1.2) - This point will be quite a bit further to the right, and just above the previous point.
5. Finally, (23, 1.4) - This point is even further along the x-axis and also above the previous point.

### Analyzing the Scatter Plot

After plotting these points, take a look at the overall trend of the data:

- The y-values increase as the x-values increase, which suggests a positive relationship.
- The increase in y-values seems to be gradual initially and appears to slow down as x increases further.

### Choosing the Best Model

- **Linear Function**: A straight line fits the data based on a consistent rate of increase. However, since the increase in y-values seems to decrease as x increases, a linear model may not fit well.
- **Exponential Function**: This would show rapid growth, not evident in the plotted data.
- **Logarithmic Function**: This suggests that y increases quickly at first but slows as x increases. This may match the behavior of the data.
- **Quadratic Function**: This is a parabolic shape and seems less likely based on the scattered points appearing more linear in form with an inflection.

### Conclusion

Based on the described visual trend of the plotted points, it seems the best fit for the data may be a **logarithmic function** because of the gradual increase rate observed. However, to finalize the model, you might consider performing curve fitting or regression analysis to determine the most accurate mathematical representation for the data.