Let's go through each bag one by one and calculate the change in circumference. The change is calculated by subtracting the initial circumference from the circumference after a certain number of minutes.
1. Bag 1:
- Initial circumference: 24 cm
- Minutes circumference: 32 cm
- Change in circumference: [tex]\(32 - 24 = 8 \)[/tex] cm
2. Bag 2:
- Initial circumference: 26 cm
- Minutes circumference: 25 cm
- Change in circumference: [tex]\(25 - 26 = -1 \)[/tex] cm
3. Bag 3:
- Initial circumference: 24 cm
- Minutes circumference: 24 cm
- Change in circumference: [tex]\(24 - 24 = 0 \)[/tex] cm
4. Bag 4:
- Initial circumference: 25 cm
- Minutes circumference: 25 cm
- Change in circumference: [tex]\(25 - 25 = 0 \)[/tex] cm
5. Bag 5:
- Initial circumference: 25 cm
- Minutes circumference: 31 cm
- Change in circumference: [tex]\(31 - 25 = 6 \)[/tex] cm
6. Bag 6:
- Initial circumference: 26 cm
- Minutes circumference: 25 cm
- Change in circumference: [tex]\(25 - 26 = -1 \)[/tex] cm
7. Bag 7:
- Initial circumference: 24 cm
- Minutes circumference: 24 cm
- Change in circumference: [tex]\(24 - 24 = 0 \)[/tex] cm
8. Bag 8:
- Initial circumference: None (Not applicable)
- Minutes circumference: None (Not applicable)
- Change in circumference: Not applicable
Now we can fill in the table based on these calculations:
[tex]\[
\begin{array}{|c|c|c|c|}
\hline
\text{Bag} & \text{Circumference, initial (cm)} & \text{Circumference, minutes (cm)} & \text{Change in circumference (cm)} \\
\hline
1 & 24 & 32 & 8 \\
\hline
2 & 26 & 25 & -1 \\
\hline
3 & 24 & 24 & 0 \\
\hline
4 & 25 & 25 & 0 \\
\hline
5 & 25 & 31 & 6 \\
\hline
6 & 26 & 25 & -1 \\
\hline
7 & 24 & 24 & 0 \\
\hline
8 & \text{N/A} & \text{N/A} & \text{N/A} \\
\hline
\end{array}
\][/tex]
