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?

Question

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?

Answer 1

To find the rate of change of the average height with respect to the number of years, we need to calculate the slope of the line that represents the relationship between these two variables.

We can choose any two points on the line and use the formula for slope:

slope = (change in average height) / (change in number of years)

Let's choose the points (1, 12) and (16, 147) from the table:

change in average height = 147 - 12 = 135
change in number of years = 16 - 1 = 15

slope = 135 / 15 = <<135/15=9>>9

Therefore, the rate of change of the average height of the trees on the farm with respect to the number of years since they were planted is 9 feet per year.