To determine which statement best describes the results of the water usage in the two storage tanks, we need to analyze the sequences of the volumes for both Tank 1 and Tank 2 as given in the table.
Let's start with Tank 1:
Time (hours) | Tank 1 (gallons)
0 | 300
1 | 240
2 | 192
3 | 153.6
4 | 122.88
We need to check if these volumes form a geometric sequence. A geometric sequence has the property that the ratio between successive terms is constant. Let's check the common ratio:
- Ratio from hour 0 to hour 1: [tex]\( \frac{240}{300} = 0.8 \)[/tex]
- Ratio from hour 1 to hour 2: [tex]\( \frac{192}{240} = 0.8 \)[/tex]
- Ratio from hour 2 to hour 3: [tex]\( \frac{153.6}{192} = 0.8 \)[/tex]
- Ratio from hour 3 to hour 4: [tex]\( \frac{122.88}{153.6} = 0.8 \)[/tex]
Since the ratio is constant (0.8), the volumes of Tank 1 form a geometric sequence.
Now, let's examine Tank 2:
Time (hours) | Tank 2 (gallons)
0 | 300
1 | 260
2 | 220
3 | 180
4 | 140
We need to check if these volumes form an arithmetic sequence. An arithmetic sequence has the property that the difference between successive terms is constant. Let's check the common difference:
- Difference from hour 0 to hour 1: [tex]\( 260 - 300 = -40 \)[/tex]
- Difference from hour 1 to hour 2: [tex]\( 220 - 260 = -40 \)[/tex]
- Difference from hour 2 to hour 3: [tex]\( 180 - 220 = -40 \)[/tex]
- Difference from hour 3 to hour 4: [tex]\( 140 - 180 = -40 \)[/tex]
Since the difference is constant (-40), the volumes of Tank 2 form an arithmetic sequence.
Summarizing the findings:
- The volume of Tank 1 forms a geometric sequence with a common ratio.
- The volume of Tank 2 forms an arithmetic sequence with a common difference.
Therefore, the correct statement is:
C. The volume of tank 2 can be represented by an arithmetic sequence because the volumes in successive hours have a common difference.
