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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

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Question:

h = 2.5 + 0.75y

A
9

explanation

The equation h = 2.5 + 0.75y represents 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. To find how many inches the tree grows each year, we can convert the height from feet to inches and then determine the change in height over one year. Since there are 12 inches in a foot, we can multiply the height in feet by 12 to convert it to inches. Let's denote the growth in inches per year as "g".

h (inches) = h (feet) × 12

g = h (inches) - (h (inches) at y-1)

To find the change in height over one year, we can substitute y and y-1 into the equation and calculate the difference:

g = (2.5 + 0.75y) × 12 - (2.5 + 0.75(y-1)) × 12

Simplifying the equation:

g = 9y - 9(y-1)

g = 9y - 9y + 9

g = 9

Therefore, the tree grows 9 inches each year.

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