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To find out how fast a tree grows, you can measure its trunk. A giant red oak's diameter was 248 inches in 1965. The tree's diameter had grown to 251 inches in 2005. Find the average rate of change in the diameter of the tree per year.

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haddles416
to find the rate of change you will want to know the independent and dependent variables. The independent variable is x and the dependent y. In this case the year that the diameter of the tree is measured is the independent variable. The equation to find the rate of change is y2-y1/x2-x1. You will want to have 2005 as y2 and 1965 as y1 because 2005 was the second time the diameter was measured. 251 would be x2 and 248 would be x1. once you substitute the numbers in you will find your rate of change. HOPE THIS WAS HELPFUL
boffeemadrid

We need to find the rate of change of diameter of a tree per year.

Change in diameter is 0.075 inches per year.

The diameter of the tree in 1965 is 248 inches.

The diameter of the tree in 2005 is 251 inches.

This situation can be modeled on the graph where the x axis is the year and y axis is the diameter

As the rate of change of diameter of a tree per year is required this means the slope is needed.

Change in y = [tex]\Delta y=251-248=3[/tex]

Change in x = [tex]\Delta x=2005-1965=40[/tex]

Slope is

[tex]m=\dfrac{\Delta y}{\Delta x}\\\Rightarrow m=\dfrac{3}{40}\\\Rightarrow m=0.075[/tex]

Change in diameter is 0.075 inches per year.

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