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To find the average rate of change of the function \( f(x) \) over the interval \( 10 \leq x \leq 15 \), we can use the formula for the average rate of change:

\[
\text{Average Rate of Change} = \frac{f(x_2) - f(x_1)}{x_2 - x_1}
\]

where:
- \( x_1 = 10 \) and \( x_2 = 15 \),
- \( f(x_1) = f(10) = 47 \),
- \( f(x_2) = f(15) = 46 \).

Plugging in these values:

\[
\text{Average Rate of Change} = \frac{46 - 47}{15 - 10} = \frac{-1}{5} = -0.2
\]

So, the average rate of change of the function over the interval \( 10 \leq x \leq 15 \) is \( -0.2 \).

Would you like further details on this solution or have any questions?

Here are five additional questions related to this topic:
1. How is the average rate of change different from the instantaneous rate of change?
2. What would the average rate of change be if the interval was \( 5 \leq x \leq 10 \)?
3. How can you interpret a negative rate of change in real-world scenarios?
4. If the values of \( f(x) \) were increasing, how would that affect the rate of change?
5. What is the significance of the rate of change being zero?

**Tip:** The average rate of change between two points on a function is simply the slope of the line connecting those points.

Given the function defined in the table below, find the average rate of change of the function over the interval 10 ≤ x ≤ 15.

Learn how to find the average rate of change of a function from a table over a specific interval, such as 10 ≤ x ≤ 15. This example covers the use of the slope formula for calculating the average rate of change, suitable for students in Grade 8.

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