Question

PLEASE HELP!!

Answer 1

Answer:  Choice A.   4 times

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Explanation:

We'll be using this formula

$m = \frac{f(b)-f(a)}{b-a}$

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.

$m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(2)-g(1)}{2-1}\\\\m = \frac{5(2)^2-5(2)^1}{2-1}\\\\m = \frac{10}{1}\\\\m = 10$

Do the same for the AROC from x = 3 to x = 4.

$m = \frac{g(b)-g(a)}{b-a}\\\\m = \frac{g(4)-g(3)}{4-3}\\\\m = \frac{5(2)^4-5(2)^3}{4-3}\\\\m = \frac{40}{1}\\\\m = 40$

The jump from m = 10 to m = 40 is "times 4", which is why choice A is the final answer.