If a tree is 10 feet tall after two years and 25 feet tall after 5 years, find the rate of change of growth of the tree if y is the height in feet and x is the number of years. Be sure to give correct units.

If a tree is 10 ft tall after 2 yr. and 25 ft. tall after 5 yr. find rate of change of growth if y is the height and x is the number of years

Well, let me branch out on this question for you. If we want to find the rate of change of the tree's growth, we can use the slope formula.

The formula for slope, or rate of change, is (change in y / change in x). So, we have the change in height - from 10 feet to 25 feet - and the change in time - from 2 years to 5 years.

Let's plug those values into the formula:
(change in y / change in x) = (25 - 10) feet / (5 - 2) years

Simplifying that, we get:
(change in y / change in x) = 15 feet / 3 years

So, the rate of change of the tree's growth is 5 feet per year. Ta-da!

To find the rate of change of growth of the tree, we need to calculate the slope of the line that represents the growth of the tree over time. The slope of a line can be determined using the formula:

slope = (change in y) / (change in x)

In this case, "y" represents the height of the tree in feet and "x" represents the number of years. We can use the given data to find the change in y and change in x.

Change in y: The tree grows from 10 feet to 25 feet, which is a change of 25 - 10 = 15 feet.

Change in x: The tree grows from 2 years to 5 years, which is a change of 5 - 2 = 3 years.

Now we can apply the formula:

slope = (change in y) / (change in x)
slope = 15 feet / 3 years

Therefore, the rate of change of growth of the tree is 15/3 = 5 feet per year.

Hence, the tree grows at a rate of 5 feet per year.

change in height = 15 feet

change in time = 5 years

growth rate (ft/yr) = 15ft/5yr = 3ft/yr

8/year