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Relationship B has a greater rate than Relationship A. This graph represents Relationship A.

What table could represent Relationship B?

Responses

Time (weeks) 2 5 6 9
Plant growth (in.) 1.2 3 3.6 5.4
Time (weeks) 2 5 6 9 Plant growth (in.) 1.2 3 3.6 5.4

Time (weeks) 2 5 6 9
Plant growth (in.) 1.6 4 4.8 7.2
Time (weeks) 2 5 6 9 Plant growth (in.) 1.6 4 4.8 7.2

Time (weeks) 2 5 6 9
Plant growth (in.) 1.4 3.5 4.2 6.3
Time (weeks) 2 5 6 9 Plant growth (in.) 1.4 3.5 4.2 6.3

Time (weeks) 3 4 6 9
Plant growth (in.) 1.5 2 3 4.5
Time (weeks) 3 4 6 9 Plant growth (in.) 1.5 2 3 4.5
First-quadrant graph showing a ray from the origin through the points begin ordered pair 4 comma 3 end ordered pair and begin ordered pair 8 comma 6 end ordered pair. Horizontal axis label is Time in weeks. Vertical axis label is Plant growth in inches.

1 answer

To determine which table could represent Relationship B, we need to identify a table that shows a greater rate of plant growth compared to the data given for Relationship A.

From the description, we do not have the specific values from Relationship A, but we can infer that Relationship B should show consistent increments in plant growth over time that are greater than those in Relationship A.

Let’s examine the provided tables for their growth rates:

  1. Table 1:

    | Time (weeks) | Plant growth (in.) | |--------------|---------------------| | 2 | 1.2 | | 5 | 3 | | 6 | 3.6 | | 9 | 5.4 |

    To find the rate of growth:

    • Growth from week 2 to week 5: \(3 - 1.2 = 1.8\) inches in 3 weeks
    • Growth from week 5 to week 6: \(3.6 - 3 = 0.6\) inches in 1 week
    • Growth from week 6 to week 9: \(5.4 - 3.6 = 1.8\) inches in 3 weeks

  2. Table 2:

    | Time (weeks) | Plant growth (in.) | |--------------|---------------------| | 2 | 1.6 | | 5 | 4 | | 6 | 4.8 | | 9 | 7.2 |

    To find the rate of growth:

    • Growth from week 2 to week 5: \(4 - 1.6 = 2.4\) inches in 3 weeks
    • Growth from week 5 to week 6: \(4.8 - 4 = 0.8\) inches in 1 week
    • Growth from week 6 to week 9: \(7.2 - 4.8 = 2.4\) inches in 3 weeks

  3. Table 3:

    | Time (weeks) | Plant growth (in.) | |--------------|---------------------| | 2 | 1.4 | | 5 | 3.5 | | 6 | 4.2 | | 9 | 6.3 |

    To find the rate of growth:

    • Growth from week 2 to week 5: \(3.5 - 1.4 = 2.1\) inches in 3 weeks
    • Growth from week 5 to week 6: \(4.2 - 3.5 = 0.7\) inches in 1 week
    • Growth from week 6 to week 9: \(6.3 - 4.2 = 2.1\) inches in 3 weeks

  4. Table 4:

    | Time (weeks) | Plant growth (in.) | |--------------|---------------------| | 3 | 1.5 | | 4 | 2 | | 6 | 3 | | 9 | 4.5 |

    To find the rate of growth:

    • Growth from week 3 to week 4: \(2 - 1.5 = 0.5\) inches in 1 week
    • Growth from week 4 to week 6: \(3 - 2 = 1\) inch in 2 weeks
    • Growth from week 6 to week 9: \(4.5 - 3 = 1.5\) inches in 3 weeks

From these analyses, Table 2 shows a consistently greater rate of growth than our estimated values from Relationship A based on the context given. Therefore, Table 2 (with values of 1.6, 4, 4.8, 7.2 for plant growth) would be the best choice to represent Relationship B.