Answer :
To determine which statement can be supported by the data provided in the table, we need to analyze the changes in height of the tree between consecutive recorded months. Let's look at the changes in height step-by-step:
1. From month 1 to month 3:
[tex]\[ \Delta h_1 = 1.5 \, \text{ft} - 1.4 \, \text{ft} = 0.1 \, \text{ft} \][/tex]
2. From month 3 to month 5:
[tex]\[ \Delta h_2 = 2.1 \, \text{ft} - 1.5 \, \text{ft} = 0.6 \, \text{ft} \][/tex]
3. From month 5 to month 7:
[tex]\[ \Delta h_3 = 2.7 \, \text{ft} - 2.1 \, \text{ft} = 0.6 \, \text{ft} \][/tex]
4. From month 7 to month 9:
[tex]\[ \Delta h_4 = 3.0 \, \text{ft} - 2.7 \, \text{ft} = 0.3 \, \text{ft} \][/tex]
5. From month 9 to month 11:
[tex]\[ \Delta h_5 = 1.8 \, \text{ft} - 3.0 \, \text{ft} = -1.2 \, \text{ft} \][/tex]
Now, let's analyze these changes:
- Between month 1 and month 3, the height increased by 0.1 ft.
- Between month 3 and month 5, the height increased by 0.6 ft.
- Between month 5 and month 7, the height increased by 0.6 ft.
- Between month 7 and month 9, the height increased by 0.3 ft.
- However, between month 9 and month 11, the height decreased by 1.2 ft.
From this analysis, we can observe that the tree increased in height in each period until the time period between month 9 and month 11, during which the height of the tree decreased.
Therefore, the statement that can be supported by the information in the table is:
- "The tree increased in height each month until the time period between month 9 and month 11."
1. From month 1 to month 3:
[tex]\[ \Delta h_1 = 1.5 \, \text{ft} - 1.4 \, \text{ft} = 0.1 \, \text{ft} \][/tex]
2. From month 3 to month 5:
[tex]\[ \Delta h_2 = 2.1 \, \text{ft} - 1.5 \, \text{ft} = 0.6 \, \text{ft} \][/tex]
3. From month 5 to month 7:
[tex]\[ \Delta h_3 = 2.7 \, \text{ft} - 2.1 \, \text{ft} = 0.6 \, \text{ft} \][/tex]
4. From month 7 to month 9:
[tex]\[ \Delta h_4 = 3.0 \, \text{ft} - 2.7 \, \text{ft} = 0.3 \, \text{ft} \][/tex]
5. From month 9 to month 11:
[tex]\[ \Delta h_5 = 1.8 \, \text{ft} - 3.0 \, \text{ft} = -1.2 \, \text{ft} \][/tex]
Now, let's analyze these changes:
- Between month 1 and month 3, the height increased by 0.1 ft.
- Between month 3 and month 5, the height increased by 0.6 ft.
- Between month 5 and month 7, the height increased by 0.6 ft.
- Between month 7 and month 9, the height increased by 0.3 ft.
- However, between month 9 and month 11, the height decreased by 1.2 ft.
From this analysis, we can observe that the tree increased in height in each period until the time period between month 9 and month 11, during which the height of the tree decreased.
Therefore, the statement that can be supported by the information in the table is:
- "The tree increased in height each month until the time period between month 9 and month 11."
