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 treat this situation as a linear relationship between time and height. The rate of change (slope) is given by the formula for the slope of a line:

$\text{slope} = \frac{\text{change in height}}{\text{change in time}} = \frac{h_2 - h_1}{t_2 - t_1}$

Where:

• $h_1 = 24$ feet (height after 3 years)
• $h_2 = 80$ feet (height after 11 years)
• $t_1 = 3$ years
• $t_2 = 11$ years

Now, plug these values into the formula:

$\text{slope} = \frac{80 - 24}{11 - 3} = \frac{56}{8} = 7 \, \text{feet per year}$

Thus, the rate of change of the average height of the trees is 7 feet per year.

Would you like more details or have any questions?

Here are 5 related questions:

1. How can you use this rate of change to predict the height of the trees after 15 years?
2. What would be the height of the trees after 0 years, assuming this rate of change holds?
3. How do you interpret a negative rate of change in such a scenario?
4. Can we model this situation with a linear equation? If so, what would the equation be?
5. How would the rate of change differ if the growth pattern was exponential rather than linear?

Tip: When dealing with word problems, always identify variables and their relationships clearly before attempting to solve the problem.