To determine the appropriate labels for the vertical axis of the graph representing the height of the dahlia plant, we first need to consider the growth rate and the time frame given.
The dahlia plant is growing at an average rate of 3 inches per week. Given that the graph represents the total height, h, of the dahlia, we can calculate the total height after a certain number of weeks:
- At week 0 (just planted), the height is 0 inches.
- At week 1, the height is 3 inches.
- At week 2, the height is 6 inches.
- At week 3, the height is 9 inches.
- At week 4, the height is 12 inches.
If we consider the height after 5 weeks, it would be:
- At week 5, the height is 15 inches.
Thus, the total height of the dahlia after \( 5 \) weeks is \( 15 \) inches.
Given the fact that we are focusing on the height from week \( 0 \) to week \( 5 \), the vertical axis needs to accommodate the complete range of heights reached, which can be from \( 0 \) inches to \( 15 \) inches ideally.
Now, let's analyze the provided options:
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10: This only goes up to 10 inches, which is not sufficient for the maximum height of 15 inches.
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2, 4, 6, 8, 10, 12, 14, 16, 18, 20: This goes up to 20 inches, which includes all required heights (0 to 15) and provides a nice increment (2 inches apart).
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3, 6, 9, 12, 15, 18, 21, 24, 27, 30: This also offers a maximum of 30 inches, but the lowest value starts at 3, which does not cover the height at week 0.
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6, 12, 18, 24, 30, 36, 42, 48, 54, 60: Again, this starts from 6 inches and continues upwards, not including the initial height of 0.
The most appropriate set of numbers representing the labels for the vertical axis on the graph, which accurately includes the growth from 0 inches to 15 inches and provides a reasonable scale for display, is the 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 option.
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