To determine how many inches the apple tree grows each year, let's analyze the given equation:
[tex]\[ h = 2.5 + 0.75y \][/tex]
Here,
- [tex]\( h \)[/tex] is the height of the tree in feet.
- [tex]\( y \)[/tex] is the number of years since the tree was planted.
- The term [tex]\( 2.5 \)[/tex] represents the initial height of the tree at the time of planting (in feet).
- The term [tex]\( 0.75y \)[/tex] represents the amount of growth for the number of years [tex]\( y \)[/tex].
To find out how many inches the tree grows each year, we need to look at the growth rate per year provided by the equation:
[tex]\[ 0.75 \][/tex]
This [tex]\( 0.75 \)[/tex] represents the growth rate in feet per year. Therefore, each year the tree grows 0.75 feet in height.
Now, let's convert this growth rate from feet to inches. We know that:
[tex]\[ 1 \text{ foot} = 12 \text{ inches} \][/tex]
Thus, to convert the growth per year from feet to inches, we multiply the growth rate in feet by the number of inches in a foot:
[tex]\[ 0.75 \text{ feet/year} \times 12 \text{ inches/foot} = 9.0 \text{ inches/year} \][/tex]
So, the tree grows 9.0 inches each year.
