For this case, the first thing we must do is define variables.
We have then:
x: number of years
y: height of the tree in feet
We write the mixed numbers as decimals:
[tex] 1 \frac{3}{4} = 1.75
[/tex]
[tex] 21 \frac{1}{4} = 21.25
[/tex]
The expression that models the problem is:
[tex] y = 1.75x + 21.25
[/tex]
By the time the tree reaches a height of 37 feet, we have:
[tex] 1.75x + 21.25 = 37
[/tex]
From here, we uncover the number of years:
[tex] 1.75x = 37 - 21.25
1.75x = 15.75
[/tex]
[tex] x = \frac{15.75}{1.75}
x = 9
[/tex]
Answer:
It will take the tree to grow from a height of 21 1/4 feet to a height of 37 feet about:
[tex] x = 9 years [/tex]
