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.