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. based on the table, which function represnts this situation
table-
1 10
3 24
6 45
11 80
15 108
answer choices
f(x) =3x+7
f(x) =-7x-3
f(x) =-3x
f(x)=7x+3
To determine which function represents the relationship between the average height of trees and the number of years since planting, we can look at the pattern in the table.
Let's look at the differences between consecutive terms for the average height:
24 - 10 = 14
45 - 24 = 21
80 - 45 = 35
108 - 80 = 28
We can see that the differences between the consecutive heights are not constant, so the relationship is not linear.
Therefore, none of the given functions represent this situation.
can you choose the right answer choice
I apologize for the oversight. Let's try to find the linear function that best fits the data provided:
From the table:
(1,10)
(3,24)
(6,45)
(11,80)
(15,108)
To determine the linear relationship, we can find the equation of the line using two points from the table. Let's use the points (1,10) and (15,108):
First, find the slope (m) using the formula:
m = (change in y)/(change in x)
m = (108 - 10)/(15 - 1)
m = 98/14
m = 7
Now that we have the slope, we can find the y-intercept (b) by using one of the points. Let's use (1,10):
10 = 7(1) + b
10 = 7 + b
b = 3
Therefore, the equation representing the linear relationship between the average height and the number of years since planting is:
f(x) = 7x + 3
So, the correct answer choice is:
f(x) = 7x + 3