Question

1. describe the growth from week to week by subtracting the height from the previous week from the current height. record the weekly growth in the third column in the table below. the median weekly growth for the dahlias from week 1 to week 2 is 3.5 inches. (i.e., 13.5 - 10 = 3.5).11. as the number of weeks increases, describe how the growth changes.12. sketch a curve through the data. when sketching a curve, do not connect the ordered pairs, but draw a smooth curve that you think reasonably describes the data.13. use the curve to estimate the median height of the dahlias at $8\frac{1}{2}$ weeks. explain how you made your estimate.14. how does the weekly growth of the dahlias in the compost beds compare to the weekly growth of the dahlias in the non-compost beds?

Explanation:

Step1: Calculate Week 3 growth

$17.75 - 13.50 = 4.25$

Step2: Calculate Week 4 growth

$21.50 - 17.75 = 3.75$

Step3: Calculate Week 5 growth

$30.50 - 21.50 = 9.00$

Step4: Calculate Week 6 growth

$40.50 - 30.50 = 10.00$

Step5: Calculate Week 7 growth

$65.00 - 40.50 = 24.50$

Step6: Calculate Week 8 growth

$80.50 - 65.00 = 15.50$

Step7: Calculate Week 9 growth

$91.50 - 80.50 = 11.00$

Step8: Analyze growth trend

List all weekly growth values: $3.5, 4.25, 3.75, 9.00, 10.00, 24.50, 15.50, 11.00$. Observe the overall upward trend with late slight decline.

Step9: Estimate 8.5 week height

Week 8 height = 80.50, Week9 height=91.50. Midpoint: $\frac{80.50 + 91.50}{2} = 86.00$

Step10: Address comparison note

No non-compost data provided.

Answer:

1. Completed Weekly Growth column values (by week):

• Week 1: –
• Week 2: 3.50
• Week 3: 4.25
• Week 4: 3.75
• Week 5: 9.00
• Week 6: 10.00
• Week 7: 24.50
• Week 8: 15.50
• Week 9: 11.00

1. As the number of weeks increases, the weekly growth generally increases (with a small decrease in the final week), showing an overall accelerating growth pattern before a slight slowdown.

1. Estimated median height at $8\frac{1}{2}$ weeks: 86.00 inches. This estimate is the midpoint between the height at week 8 (80.50 inches) and week 9 (91.50 inches), assuming linear growth between these two weeks.

1. No data about the weekly growth of dahlias in non-compost beds is provided, so a comparison cannot be made.