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:
\(1 \frac{3}{4} = 1.75
\)
\(21 \frac{1}{4} = 21.25
\)
The expression that models the problem is:
\(y = 1.75x + 21.25
\)
By the time the tree reaches a height of 37 feet, we have:
\(1.75x + 21.25 = 37
\)
From here, we uncover the number of years:
\(1.75x = 37 - 21.25
1.75x = 15.75
\)
\(x = \frac{15.75}{1.75}
x = 9
\)
Answer:
It will take the tree to grow from a height of 21 1/4 feet to a height of 37 feet about:
\(x = 9 years\)
