Let's examine the relationship between the number of files and the storage space used in megabytes (Mb). We have the following pairs:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Number of Files} & \text{Space Used (Mb)} \\
\hline
10 & 15 \\
\hline
20 & 30 \\
\hline
30 & 45 \\
\hline
40 & 60 \\
\hline
50 & 75 \\
\hline
\end{array}
\][/tex]
We will analyze these pairs to determine the relationship between the number of files and the space used. Let's compare the increase in space used for each increase in the number of files:
1. From 10 files to 20 files, space used increases from 15 Mb to 30 Mb.
2. From 20 files to 30 files, space used increases from 30 Mb to 45 Mb.
3. From 30 files to 40 files, space used increases from 45 Mb to 60 Mb.
4. From 40 files to 50 files, space used increases from 60 Mb to 75 Mb.
Notice that every time the number of files increases by 10, the storage space used increases by 15 Mb. This indicates a linear relationship where the ratio of the space used (Mb) to the number of files remains consistent. Specifically:
[tex]\[
\frac{15}{10} = \frac{30}{20} = \frac{45}{30} = \frac{60}{40} = \frac{75}{50} = 1.5 \text{ (Mb per file)}
\][/tex]
Hence, the rate of storage space used per file is constant at 1.5 Mb per file.
Given that each time the number of files increases, the storage space used also increases, the relationship between the number of files and the storage space used is positive and linear. Therefore, the statement that best describes this data is:
"As the number of files increases, the storage space used increases."
