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
A. 9ft/yr
B. 27ft/yr
C. 3ft/yr
D. 12ft/yr
To determine the rate of change in height per year, we need to find the difference in average height divided by the difference in number of years for each pair of data points.
For the first pair (1 year and 4 years), the average height increased by 39-12 = 27 ft. The number of years increased by 4-1 = 3 years. Therefore, the rate of change is 27 ft/ 3 years = 9 ft/yr.
For the second pair (4 years and 9 years), the average height increased by 84-39 = 45 ft. The number of years increased by 9-4 = 5 years. Therefore, the rate of change is 45 ft/ 5 years = 9 ft/yr.
For the third pair (9 years and 16 years), the average height increased by 147-84 = 63 ft. The number of years increased by 16-9 = 7 years. Therefore, the rate of change is 63 ft/ 7 years = 9 ft/yr.
Since the rate of change in average height per year is the same for all the pairs, the answer is A. 9 ft/yr.