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](https://tex.z-dn.net/?f=%201%20%5Cfrac%7B3%7D%7B4%7D%20%3D%201.75%20%20%20)
![21 \frac{1}{4} = 21.25](https://tex.z-dn.net/?f=%2021%20%5Cfrac%7B1%7D%7B4%7D%20%3D%2021.25%20%20%20)
The expression that models the problem is:
![y = 1.75x + 21.25](https://tex.z-dn.net/?f=%20y%20%3D%201.75x%20%2B%2021.25%20%20)
By the time the tree reaches a height of 37 feet, we have:
![1.75x + 21.25 = 37](https://tex.z-dn.net/?f=%201.75x%20%2B%2021.25%20%3D%2037%20%20)
From here, we uncover the number of years:
![1.75x = 37 - 21.25\\1.75x = 15.75](https://tex.z-dn.net/?f=%201.75x%20%3D%2037%20-%2021.25%5C%5C1.75x%20%3D%2015.75%20%20)
![x = \frac{15.75}{1.75}\\x = 9](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cfrac%7B15.75%7D%7B1.75%7D%5C%5Cx%20%3D%209%20%20%20)
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](https://tex.z-dn.net/?f=%20x%20%3D%209%20years%20)