Math  /  Data & Statistics

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Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 2x82 \leq x \leq 8. \begin{tabular}{|c|c|} \hlinexx & f(x)f(x) \\ \hline 2 & 7 \\ \hline 4 & 15 \\ \hline 6 & 31 \\ \hline 8 & 55 \\ \hline 10 & 87 \\ \hline \end{tabular}
Answer Attempt 1 out of 2 \square Submit Answer

Studdy Solution
Apply the average rate of change formula:
Average rate of change=f(8)f(2)82\text{Average rate of change} = \frac{f(8) - f(2)}{8 - 2}
Substitute the known values:
55782=486\frac{55 - 7}{8 - 2} = \frac{48}{6}
Simplify the fraction:
486=8\frac{48}{6} = 8
The average rate of change of the function over the interval 2x82 \leq x \leq 8 is:
8 \boxed{8}

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