the table shows the linear relationship between the average height in feet of trees on a tree farm and the number of years since the trees were planted.
Number of Years Since the Trees Were Planted
Average Height (ft)
1
12
4
39
9
84
16
147
From the given table, we can observe that as the number of years since the trees were planted increases, the average height of the trees also increases.
To better understand the relationship, we can calculate the average height increase per year. By finding the difference in average height between consecutive years and dividing it by the number of years elapsed.
Between year 1 and year 4: 39 - 12 = 27 ft increase
Years elapsed: 4 - 1 = 3 years
Average height increase per year: 27 ft / 3 years = 9 ft/year
Between year 4 and year 9: 84 - 39 = 45 ft increase
Years elapsed: 9 - 4 = 5 years
Average height increase per year: 45 ft / 5 years = 9 ft/year
Between year 9 and year 16: 147 - 84 = 63 ft increase
Years elapsed: 16 - 9 = 7 years
Average height increase per year: 63 ft / 7 years = 9 ft/year
As we can observe, the average height increase per year remains consistent at 9 ft/year throughout the given time period. Therefore, we can conclude that there is a linear relationship between the average height of the trees and the number of years since they were planted, with an average height increase of 9 ft/year.