Answer: The correct option is (B) 27.5.
Step-by-step explanation: We are given to find the average rate of change of the function described in the table for the interval x = 2 to x = 4.
We know that
the average rate of change of a function y = f(x) for the interval x = a to x = b is given by
[tex]A_v=\dfrac{f(b)-f(a)}{b-a}.[/tex]
From the table, we note that for the given function
f(2) = 9 and f(4) = 64.
Therefore, the average rate of change of the given function for the interval x = 2 to x = 4 is
[tex]A_v=\dfrac{f(4)-f(2)}{4-2}=\dfrac{64-9}{4-2}=\dfrac{55}{2}=27.5.[/tex]
Thus, the required average rate of change is 27.5.
Option (B) is CORRECT.
