To analyze the relationship between the number of music files and the storage space used, let's carefully examine the data in the table provided:
```
Number of Files Space Used (Mb)
10 15
20 30
30 45
40 60
50 75
```
Step-by-step Analysis:
1. Observe the Data Pairs: We have pairs of data points for the number of files and corresponding storage space used.
2. Identify the Trend:
- 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.
3. Notice the Consistent Relationship:
- Each time the number of files increases by 10, the space used increases by 15 Mb.
- This suggests a linear relationship where the space used grows at a constant rate with the increase in the number of files.
4. Calculate the Rate of Change: The rate at which the space used increases per additional file is determined by taking the difference in space used and dividing it by the difference in the number of files:
[tex]\[
\text{Rate of Change} = \frac{75 - 15}{50 - 10} = \frac{60}{40} = 1.5 \text{ Mb per file}
\][/tex]
5. Determine the Relationship Statement:
- As we see from the data, each time the number of files increases, the storage space also increases.
- Hence, the last statement in the list is the correct one.
Conclusion:
The best description of the relationship between storage space and the number of music files is:
As the number of files increases, the storage space used increases.
