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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.

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 24 ≤ x ≤ 96.

This problem involves finding the average rate of change of a function from the table over the interval 24 ≤ x ≤ 96. It utilizes the formula for the rate of change between two points and explains key concepts such as secant lines. Ideal for students in Grades 9-11.

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