A tree grows 1 3/4 per year.
[tex]1\frac{3}{4} = \frac{7}{4}[/tex]
Rate of growth =slope(m) =[tex]\frac{7}{4}[/tex] feet per year
Initial height = [tex]21\frac{1}{4} = \frac{85}{4}[/tex] feet
Final height = 37 feet
Since there is a constant growth every year , we use linear equation
y= mx+b
Where x is the number of years
b is the initial height and y is the final height
We know the value of m, y and b
Plug in all the values
37 = [tex]\frac{7}{4}[/tex]* x + [tex]\frac{85}{4}[/tex]
Now we solve for x, subtract the fraction 85/4 on both sides
37 - [tex]\frac{85}{4}[/tex] = [tex]\frac{7}{4}[/tex]* x
[tex]\frac{148-85}{4}[/tex]=[tex]\frac{7}{4}[/tex]* x
[tex]\frac{63}{4}[/tex]=[tex]\frac{7}{4}[/tex]* x
Multiply both sides by 4/7
[tex]\frac{63}{4}[/tex]*[tex]\frac{4}{7}[/tex]=* x
9 = x
So, it will take 9 years to grow to the height of 37 feet.
