To solve the problem, we need to find the average rate of change of the function $f(x)$ over the interval $24 \leq x \leq 96$. The average rate of change is given by the formula:

$\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}$

Where $a = 24$ and $b = 96$.

From the table provided:

• $f(24) = 50$
• $f(96) = 38$

Substituting these values into the formula:

$\text{Average Rate of Change} = \frac{f(96) - f(24)}{96 - 24} = \frac{38 - 50}{96 - 24} = \frac{-12}{72} = -\frac{1}{6}$

So, the average rate of change of the function over the interval $24 \leq x \leq 96$ is $-\frac{1}{6}$.

Would you like more details on this, or do you have any questions?

Here are five questions that expand on this topic:

1. What is the significance of a negative average rate of change?
2. How would the rate of change differ if we used a different interval, such as $42 \leq x \leq 96$?
3. Can you explain how the average rate of change relates to the slope of a line?
4. How can we interpret the average rate of change in a real-world scenario?
5. What does it mean if the average rate of change is zero over an interval?

Tip: The average rate of change of a function over an interval is equivalent to the slope of the secant line passing through the points corresponding to the endpoints of the interval.