Final answer:
The average rate of change of the function f(x) = 2(3)^x from x = 2 to x = 4 is 72, which is not listed among the provided options.
Step-by-step explanation:
The average rate of change of the function f(x) = 2(3)^x from x = 2 to x = 4 is calculated using the formula for average rate of change, which is:
Average rate of change = (f(b) - f(a)) / (b - a)
Substituting the given function and values into this formula, we have:
f(4) = 2(3)^4 = 2(81) = 162
f(2) = 2(3)^2 = 2(9) = 18
Now, use these values to find the average rate of change:
Average rate of change = (f(4) - f(2)) / (4 - 2) = (162 - 18) / 2 = 144 / 2 = 72
Thus, the correct answer is none of the options given as the average rate of change is 72.