5

Set 4: Exponential Functions (Intermediate)

Explanation

Answer: A

A wildfire burns 2 acres on hour 1, 8 acres on hour 2, 32 acres on hour 3. How many acres total burned after 5 hours?

A.

682 acres

✓ Correct
B.

512 acres

C.

242 acres

D.

1,024 acres

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Find the pattern and sum. 1. Pattern: 2,8,32,...2, 8, 32, ... means multiply by 4 each hour: A(h)=2(4)h1A(h) = 2(4)^{h-1}. 2. Calculate Each Hour: - Hour 1: 2 - Hour 2: 8 - Hour 3: 32 - Hour 4: 128 - Hour 5: 512 3. Total: 2+8+32+128+512=6822+ 8 + 32 + 128 + 512 = 682 acres. Strategic Tip: Sum a geometric series: a(rn1r1)a(\frac{r^n - 1}{r - 1}) or calculate each term. Choice B is incorrect because this is just hour 5, not the total. Choice C is incorrect because this is the sum of only hours 1-4. Choice D is incorrect because this would be hour 6.

Key Steps:

The correct answer is 682 acres

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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