Answer: Choice A. 4 times
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Explanation:
We'll be using this formula
[tex]m = \frac{f(b)-f(a)}{b-a}[/tex]
to compute the average rate of change (AROC) from x = a to x = b. Note how this is effectively the slope formula because y = f(x).
To start things off, we'll compute the AROC from x = 1 to x = 2.
[tex]m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(2)-g(1)}{2-1}\\\\m = \frac{5(2)^2-5(2)^1}{2-1}\\\\m = \frac{10}{1}\\\\m = 10\\\\[/tex]
Do the same for the AROC from x = 3 to x = 4.
[tex]m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(4)-g(3)}{4-3}\\\\m = \frac{5(2)^4-5(2)^3}{4-3}\\\\m = \frac{40}{1}\\\\m = 40\\\\[/tex]
The jump from m = 10 to m = 40 is "times 4", which is why choice A is the final answer.
