Question

1. a function is shown.

$g(x) = 61,300(.08)^x$

to the nearest whole number, what is the average rate of change of the function over the interval from $x = 1$ to $x = 3$?

• -2,436
• -4,522
• -563,699
• -29

Explanation:

Step1: Calculate g(1)

$g(1) = 61300(0.8)^1 = 61300×0.8 = 49040$

Step2: Calculate g(3)

$g(3) = 61300(0.8)^3 = 61300×0.512 = 31385.6$

Step3: Compute average rate of change

Average rate = $\frac{g(3)-g(1)}{3-1} = \frac{31385.6 - 49040}{2} = \frac{-17654.4}{2} = -8827.2$? Wait, no—wait, 0.8 cubed is 0.8×0.8×0.8=0.512, yes. 61300×0.512: 61300×0.5=30650, 61300×0.012=735.6, total 30650+735.6=31385.6. Correct. Then 31385.6-49040=-17654.4, divided by 2 is -8827.2? But the options don't have this. Wait, did I misread the function? Oh wait, is it 61.300? No, the problem says 61,300. Wait, no—wait, maybe the function is 61300(0.08)^x? Let's check: 0.08^1=0.08, so g(1)=61300×0.08=4904; g(3)=61300×(0.08)^3=61300×0.000512=31.3856. Then average rate=(31.3856-4904)/2≈(-4872.6144)/2≈-2436.3072, which is -2436 when rounded. That's option 1. Oh, probably a typo in my initial reading—0.08 instead of 0.8. Yes, that matches the option.

Answer:

-2,436