To estimate the average rate of change of a function over an interval \([a, b]\), you can use the formula:
\[ \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a} \]
In your case, the interval is \([5.13, 8.77]\). However, to calculate the average rate of change, we need to know the values of the function \(f(x)\) at \(x = 5.13\) and \(x = 8.77\).
If you can provide the function \(f(x)\) or its values at the specified points, I would be happy to help you compute the average rate of change!