Laura planted trees as a hobby at a tree farm. She records the average height in feet of trees and the number of years since the trees were planted. She noticed after 3 years the average height was 24 feet. She also recorded after 11 years the average height was 80 feet. What is the rate of change of the average height in feet of the trees on the farm with respect to the number of years since the trees were planted?

A.14 feet per year

B.3 feet per year

C.7 feet per year

D.10 feet per year


To find the rate of change of the average height of the trees with respect to the number of years since they were planted, we can calculate the slope of the line that passes through the two points given: \((3, 24)\) and \((11, 80)\).

The formula for the slope (rate of change) \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the given values:

\[
m = \frac{80 - 24}{11 - 3} = \frac{56}{8} = 7 \text{ feet per year}
\]

So, the rate of change of the average height of the trees with respect to the number of years since they were planted is **7 feet per year**.

The correct answer is:

**C. 7 feet per year**

Would you like details on the calculation process, or do you have any questions?

Here are 5 related questions you might find useful:
1. How do you interpret the rate of change in a linear relationship?
2. What is the significance of the slope in the context of real-life situations?
3. How can you determine if two quantities have a linear relationship?
4. What does it mean if the rate of change is zero?
5. How would the problem change if the growth rate was not constant?

**Tip:** Always check the units in word problems to ensure your calculations are correct.

Understand how to calculate the rate of change of the average height of trees over years with a step-by-step solution. Given data points include 3 years at 24 feet and 11 years at 80 feet. Learn the slope formula and its application. Suitable for students in Grades 7-9.

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