Answer:
The birch tree needs 12 years
Step-by-step explanation:
Proportional Relationship
Two variables t and d are proportional if they have the relationship described by the equation:
d = kt
Where k is the constant of proportionality.
From the graph on the question, we recognize the proportionality of the age of a birch tree and its diameter because the line passes through the origin (0,0). To find the equation, we need to recognize a clear point on the graph. We select the point (2,7). Substituting in the equation:
7 = 2k
Thus:
[tex]k=\frac{7}{2}[/tex]
The equation is:
[tex]\displaystyle d=\frac{7}{2}t[/tex]
For the birch to have a diameter of d=42 inches, the time needed can be calculated by solving the equation:
[tex]\displaystyle 42=\frac{7}{2}t[/tex]
[tex]\displaystyle t=42*\frac{2}{7}[/tex]
t = 12 years
The birch tree needs 12 years
