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
What is the rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted?
To find the rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted, we need to determine the slope of the linear relationship between the two variables.
We can calculate the slope by using the formula:
Slope = (Change in Average Height) / (Change in Number of Years since the Trees were Planted)
Let's calculate the change in average height for each interval:
Change in Average Height (12 - 0) = 12 - 0 = 12
Change in Average Height (39 - 12) = 39 - 12 = 27
Change in Average Height (84 - 39) = 84 - 39 = 45
Change in Average Height (147 - 84) = 147 - 84 = 63
Next, let's calculate the change in the number of years since the trees were planted for each interval:
Change in Number of Years (4 - 1) = 4 - 1 = 3
Change in Number of Years (9 - 4) = 9 - 4 = 5
Change in Number of Years (16 - 9) = 16 - 9 = 7
Now, let's calculate the slope using the formula mentioned earlier:
Slope = (12 + 27 + 45 + 63) / (3 + 5 + 7)
Slope = 147 / 15
Slope = 9.8
Therefore, the rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted is 9.8 ft/year.