9
advanced-math

A pond's algae coverage doubles every 3 days. If it covers 5% of the pond today, when will it cover 100%?

A

About 13 days

B

60 days

C

30 days

D

20 days

Correct Answer: A

Choice A is the correct answer. Find when coverage goes from 5% to 100%.

  1. Growth Needed: 1005=20\frac{100}{5} = 20 times larger.
  2. Doublings: 2024=1620 \approx 2^4 = 16 (close) to 25=322^5 = 32. Actually 2020 is between 24=162^4=16 and 25=322^5=32, closer to 24.322^{4.32}.
  3. Time: About 4-5 doublings ×\times 3 days = 12-15 days.
  4. More precise: 2x=202^x = 20, so x4.32x \approx 4.32 doublings, thus 4.32×3134.32 \times 3 \approx 13 days.

💡 Strategic Tip: To grow by factor of 20, need log2(20)4.32\log_2(20) \approx 4.32 doublings.

Choice B is incorrect because doubling is much faster. Choice C is incorrect because this assumes 10 doublings. Choice D is incorrect because this doesn't match the calculation.