To determine which data set can reasonably be modeled by a linear relationship, we should first analyze the nature of each data set based on its coordinates:
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Data Set A: (0,2), (1,4), (2,8), (3,16), (4,32), (5,64)
- The y-values are increasing rapidly, suggesting an exponential or quadratic relationship.
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Data Set B: (3,4), (4,6), (5,8), (6,10), (7,12)
- The y-values increase by a constant rate (2), indicating a linear relationship. This looks linear.
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Data Set C: (0,1), (3,3), (6,9), (9,27), (12,81)
- Although there is some increase, especially between (9,27) and (12,81), it appears more exponential due to the drastic increase in y-values.
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Data Set D: (2,4), (−1,2), (7,16), (−4,32), (1,64)
- The y-values do not show a linear trend as they vary non-uniformly.
Based on this analysis, Data Set B is the only one that can be reasonably modeled by a linear relationship, as it shows a consistent increase in y-values corresponding to a consistent increase in x-values.
Thus, the answer is: Data Set B