A tree grows 1 3/4 per year.
\(1\frac{3}{4} = \frac{7}{4}\)
Rate of growth =slope(m) =\(\frac{7}{4}\) feet per year
Initial height = \(21\frac{1}{4} = \frac{85}{4}\) 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 = \(\frac{7}{4}\) x + \(\frac{85}{4}\)
Now we solve for x, subtract the fraction 85/4 on both sides
37 - \(\frac{85}{4}\) = \(\frac{7}{4}\) x
\(\frac{148-85}{4}\)=\(\frac{7}{4}\) x
\(\frac{63}{4}\)=\(\frac{7}{4}\) x
Multiply both sides by 4/7
\(\frac{63}{4}\)\(\frac{4}{7}\)= x
9 = x
So, it will take 9 years to grow to the height of 37 feet.
