The table below lists different amounts (metric tons) of explosives and the corresponding value on the Richter scale for the explosions. Construct a scatterplot and identify the mathematical model that best fits the given data. x (metric tons) 3 12 17 43 114 463 y (Richter scale) 2.9 3.8 4.1 4.4 4.6 5.1

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### Analyzing the Relationship Between Explosives and Richter Scale Readings

#### Problem Statement

The table below lists different amounts (in metric tons) of explosives and the corresponding values on the Richter scale for the explosions. Our objective is to construct a scatter plot and identify the mathematical model that best fits the given data.

| x (metric tons) | 3 | 12 | 17 | 43 | 114 | 463 |
|-----------------|----|----|----|----|-----|-----|
| y (Richter scale)| 2.9 | 3.8 | 4.1 | 4.4 | 4.6 | 5.1 |

#### Task

Choose the correct scatter plot below:

- **Option A:**
  ![Graph X](link to graph A)
- **Option B:**
  ![Graph Y](link to graph B)
- **Option C:**
  ![Graph Z](link to graph C)
- **Option D:**
  ![Graph W](link to graph D)

#### Graph Descriptions

1. **Graph A:**
   A plot where the x-axis (horizontal) represents the amount of explosives in metric tons, ranging from 0 to 600. The y-axis (vertical) illustrates the corresponding values on the Richter scale, with values ranging from 2.5 to 5.5.

2. **Graph B:**
   A similar plot as Graph A, with the x-axis ranging from 0 to 600 and the y-axis ranging from 2.5 to 5.5.

3. **Graph C:**
   Another similar plot where the x-axis ranges from 0 to 600 and the y-axis from 2.5 to 5.5.

4. **Graph D:**
   Also a plot with the x-axis spanning from 0 to 600 and the y-axis from 2.5 to 5.5.

Each graph is intended to represent the relationship between the amount of explosives and the resultant values on the Richter scale. You need to choose the graph that correctly represents the dataset provided.

#### Analysis of Scatter Plots

1. **Identifying Trends:**
    - Examine the pattern and distribution of the points.
    - Check if the points form a recognizable trend (e.g., linear, exponential).

2. **Mathematical Models:**
    - Determine if the data fits a
Transcribed Image Text:### Analyzing the Relationship Between Explosives and Richter Scale Readings #### Problem Statement The table below lists different amounts (in metric tons) of explosives and the corresponding values on the Richter scale for the explosions. Our objective is to construct a scatter plot and identify the mathematical model that best fits the given data. | x (metric tons) | 3 | 12 | 17 | 43 | 114 | 463 | |-----------------|----|----|----|----|-----|-----| | y (Richter scale)| 2.9 | 3.8 | 4.1 | 4.4 | 4.6 | 5.1 | #### Task Choose the correct scatter plot below: - **Option A:** ![Graph X](link to graph A) - **Option B:** ![Graph Y](link to graph B) - **Option C:** ![Graph Z](link to graph C) - **Option D:** ![Graph W](link to graph D) #### Graph Descriptions 1. **Graph A:** A plot where the x-axis (horizontal) represents the amount of explosives in metric tons, ranging from 0 to 600. The y-axis (vertical) illustrates the corresponding values on the Richter scale, with values ranging from 2.5 to 5.5. 2. **Graph B:** A similar plot as Graph A, with the x-axis ranging from 0 to 600 and the y-axis ranging from 2.5 to 5.5. 3. **Graph C:** Another similar plot where the x-axis ranges from 0 to 600 and the y-axis from 2.5 to 5.5. 4. **Graph D:** Also a plot with the x-axis spanning from 0 to 600 and the y-axis from 2.5 to 5.5. Each graph is intended to represent the relationship between the amount of explosives and the resultant values on the Richter scale. You need to choose the graph that correctly represents the dataset provided. #### Analysis of Scatter Plots 1. **Identifying Trends:** - Examine the pattern and distribution of the points. - Check if the points form a recognizable trend (e.g., linear, exponential). 2. **Mathematical Models:** - Determine if the data fits a
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