Question

The graph shows the relationship between the height of a tree and its age in years. What is the unit rate of growth for the tree?

A. 0.25 feet per year
B. 0.5 feet per year
C. 2 feet per year
D. 3 feet per year

Answer 1

Option (c) is corrrect.

The unit rate of growth for the tree is 2 feet per year.

Explanation:

Given : A graph showing the relationship between the height of a tree and its age in years.

We have to find the unit rate of growth for the tree.

Consider the given graph.

Since, the slope of the graph gives the rate of change occurring per year.

Here, The slope will give the unit rate of growth for the tree.

Consider two points on the equation of line,

(1,2) and (2,4)

Slope between two points is given by ,

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(1,\:2\right),\:\left(x_2,\:y_2\right)=\left(2,\:4\right)`

Subsitute, we have,

`m=(4-2)/(2-1)=2`

Thus, The unit rate of growth for the tree is 2 feet per year.

Answer 2

C. 2 feet per year
Hope this helps!