To analyze the relationship between the number of music files and the storage space used, let us examine the data given in the table:
| Number of Files | Space Used (MB) |
|-----------------|-----------------|
| 10 | 15 |
| 20 | 30 |
| 30 | 45 |
| 40 | 60 |
| 50 | 75 |
We can observe the following points step-by-step:
1. Step-by-step Analysis:
- When the number of files is 10, the space used is 15 MB.
- When the number of files is 20, the space used is 30 MB.
- When the number of files is 30, the space used is 45 MB.
- When the number of files is 40, the space used is 60 MB.
- When the number of files is 50, the space used is 75 MB.
2. Identifying the Relationship:
- Notice how when the number of files increases from 10 to 20, the space used increases from 15 MB to 30 MB.
- Similarly, when the number of files increases from 20 to 30, the space used increases from 30 MB to 45 MB.
- The pattern continues as the number of files increases from 30 to 40, and from 40 to 50, resulting in increases in space used to 60 MB and 75 MB respectively.
3. Calculating the Rate of Change:
- Let's calculate the change in space used per 10 files:
[tex]\[
\text{Rate of Change} = \frac{\text{Increase in Space Used}}{\text{Increase in Number of Files}}
\][/tex]
- From 10 files to 20 files: [tex]\(\frac{30 - 15}{20 - 10} = \frac{15}{10} = 1.5 \text{ MB per file}\)[/tex]
- From 20 files to 30 files: [tex]\(\frac{45 - 30}{30 - 20} = \frac{15}{10} = 1.5 \text{ MB per file}\)[/tex]
- From 30 files to 40 files: [tex]\(\frac{60 - 45}{40 - 30} = \frac{15}{10} = 1.5 \text{ MB per file}\)[/tex]
- From 40 files to 50 files: [tex]\(\frac{75 - 60}{50 - 40} = \frac{15}{10} = 1.5 \text{ MB per file}\)[/tex]
4. Conclusion:
- The rate of change is consistent at 1.5 MB per file, indicating a linear relationship.
- Therefore, the space used increases by 1.5 MB for each additional file added.
Based on this analysis, we can conclude that:
As the number of files increases, the storage space used increases.
This relationship is consistent throughout the table, making it clear that the statement "As the number of files increases, the storage space used increases." best describes the relationship between storage space and the number of music files.
