To determine which function has the greatest rate of change, we can look at the slopes of the functions represented.
For option B, the points (6, 7) and (0, 2) indicate that it's a linear relationship, so we can calculate the slope of the line through those points:
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Calculate the slope for option B: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{6 - 0} = \frac{5}{6} \approx 0.8333 \]
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Option D provides specific values: We can compute the average rate of change between each pair of points:
- From (0, 2.50) to (2, 4.03): \[ \text{slope} = \frac{4.03 - 2.50}{2 - 0} = \frac{1.53}{2} \approx 0.765 \]
- From (2, 4.03) to (4, 5.56): \[ \text{slope} = \frac{5.56 - 4.03}{4 - 2} = \frac{1.53}{2} \approx 0.765 \]
- From (4, 5.56) to (6, 7.09): \[ \text{slope} = \frac{7.09 - 5.56}{6 - 4} = \frac{1.53}{2} \approx 0.765 \]
The average rate of change is consistent across the intervals, yielding a slope of approximately 0.765.
Comparing these results:
- Option B: ~0.8333
- Option D: ~0.765
Thus, option B has the greatest rate of change based on the calculated slopes.
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