Question

What is the average rate of change of the function f(x) = 2(3)^x from x = 2 to x = 4?

a) 6
b) 3
c) 9
d) 12

Answer 1

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.