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 calculate the slope of the linear relationship between the number of years and the height of the trees.

The slope formula is:

$\text{Slope} = \frac{\Delta y}{\Delta x} = \frac{\text{Change in Height}}{\text{Change in Time}}$

Given:

• After 3 years, the height is 24 feet.
• After 11 years, the height is 80 feet.

Now, calculate the change in height and the change in time:

$\Delta \text{Height} = 80 \, \text{feet} - 24 \, \text{feet} = 56 \, \text{feet}$ $\Delta \text{Time} = 11 \, \text{years} - 3 \, \text{years} = 8 \, \text{years}$

Now, calculate the slope:

$\text{Slope} = \frac{56 \, \text{feet}}{8 \, \text{years}} = 7 \, \text{feet per year}$

Therefore, 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 more details or have any questions?

Here are some related questions you might find interesting:

1. How would you calculate the expected height after 15 years using the rate of change?
2. What would the height be if the trees had been planted for 0 years?
3. Can you derive a linear equation to represent this relationship?
4. How does this rate of change compare to other growth rates you might know of in different plants?
5. What factors could affect the linearity of this growth over a longer period?

Tip: Always pay attention to units when calculating rates of change. The slope formula gives you a "per unit" rate that helps to understand the relationship between two variables.