Construct a table of values that shows the height of a birch tree.
A
Nonlinear function.
B
The birch tree, see solution.
Practice makes perfect
Consider the given table that shows the height h in feet of a willow tree after x years.
Years, x
Height, h
0
5
1
11
4
17
9
23
The value of x and its corresponding value of y represent a ordered pair that can be plotted in a coordinate plane.
We want to know if the table represents a linear or nonlinear function. Recall that the graph of a linear function shows a constant rate of change and is always a straight line. A nonlinear function does not have a constant rate of change, so its graph is not a line. Let's see some examples of different lines!
We cannot draw a straight line that passes through the given points.
Therefore, the table represents a nonlinear function.
We are told that a birch tree is 9 feet tall and grows at a rate of 2 feet per year. To find which tree is taller after 10 years, we will construct a table of values that represents the height h of the birch tree after x years. Start with x=0 and y=9, then add 2 feet per year.
Years, x
Height, h
0
9
1
11
4
17
9
27
10
29
The birch tree will be 29 feet tall after 10 years. As we can see in Part A, there is no linear relationship between the height of the willow tree and the years. Let's expand our table to show the growth of both trees.
Years
Birch Height (ft)
Willow Height (ft)
0
9
5
1
11
11
4
17
17
9
27
23
10
29
?
However, the willow tree only grew 6 feet between years 4 and 9, a five-year span. It is unlikely that the tree will grow over 6 feet to overtake the birch between years 9 and 10. While we cannot be certain, we can make an educated guess that the birch tree will be taller after 10 years.
