What is the rate of change of the average height in feet of the trees with respect to the number of years since the trees were planted? *
average tree height
numbers of years trees were planted 1,3,6,11,15
average height 10,24,45,80,108
3 ft/yr
7 ft/yr
10 ft/yr
14 ft/yr
The answer is 7
To find the rate of change of the average height of the trees with respect to the number of years since the trees were planted, we need to calculate the difference in average height and the difference in number of years for each pair of data points.
First, let's calculate the differences:
Difference in average height:
24 - 10 = 14 ft
45 - 24 = 21 ft
80 - 45 = 35 ft
108 - 80 = 28 ft
Difference in number of years:
3 - 1 = 2 years
6 - 3 = 3 years
11 - 6 = 5 years
15 - 11 = 4 years
Next, we will divide the difference in average height by the difference in number of years to find the rate of change:
14 ft / 2 years = 7 ft/yr
21 ft / 3 years = 7 ft/yr
35 ft / 5 years = 7 ft/yr
28 ft / 4 years = 7 ft/yr
Therefore, the rate of change of the average height in feet of the trees with respect to the number of years since the trees were planted is 7 ft/yr.
To find the rate of change of the average height of the trees with respect to the number of years since they were planted, we need to calculate the average rate of change between each pair of data points.
Let's calculate the average rate of change between the first two data points:
Average rate of change between the first two data points = (change in average height) / (change in number of years)
= (24 ft - 10 ft) / (3 years - 1 year)
= 14 ft / 2 years
= 7 ft/yr
Similarly, we can calculate the average rate of change between the other pairs of data points:
Average rate of change between the second pair of data points: (45 ft - 24 ft) / (6 years - 3 years) = 21 ft / 3 years = 7 ft/yr
Average rate of change between the third pair of data points: (80 ft - 45 ft) / (11 years - 6 years) = 35 ft / 5 years = 7 ft/yr
Average rate of change between the fourth pair of data points: (108 ft - 80 ft) / (15 years - 11 years) = 28 ft / 4 years = 7 ft/yr
As we can see, the average rate of change is consistent at 7 ft/yr. Therefore, the rate of change of the average height in feet of the trees with respect to the number of years since they were planted is 7 ft/yr.
If you plot the points you can drop a triangle to find the rise and run and slope is rise/run
also
rate of change = (y2-y1)/(x2-x1)
(1,10) (3,24)
(x1,y1) (x2,y2)
= (24-10)/(3-1)
and the answer is in the list of answers : )