4
advanced-math

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

B

512 acres

C

242 acres

D

1,024 acres

Correct Answer: A

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.