Question

1. the equation below calculates the growth of an apple tree, where \\(h\\) is the height in feet and \\(y\\) is the number of years since the tree was planted. how many inches does the tree grow each year?

\\h = 2.5 + 0.75y\\

• 0.75
• 2.5
• 9
• 30

Explanation:

Identify the given equation and variables

The given linear equation modeling the height of the apple tree is:

$$h = 2.5 + 0.75y$$

where:

• \(h\) is the height of the tree in feet.
• \(y\) is the number of years since the tree was planted.

Determine the growth rate in feet per year

In a linear equation of the form \(h = a + by\), the coefficient \(b\) represents the rate of change.
Here, \(b = 0.75\).
This means the tree grows at a rate of \(0.75\) feet each year.

Convert the growth rate from feet to inches

The question asks for the growth in inches each year.
We use the conversion factor:

$$1\text{ foot} = 12\text{ inches}$$

Multiply the growth rate in feet by \(12\):

$$\text{Growth per year} = 0.75 \times 12$$

Calculate the final value

Perform the multiplication:

$$0.75 \times 12 = \frac{3}{4} \times 12 = 3 \times 3 = 9$$

Thus, the tree grows \(9\) inches each year.

Answer:

• 0.75
• 2.5
• 9 (Correct answer)
• 30