10
advanced-math

A battery loses 5% of its charge per day. Starting at 100%, after how many days will it be below 80%?

A

5 days

B

4 days

C

3 days

D

6 days

Correct Answer: A

Choice A is the correct answer. Find when charge drops below 80%.

  1. Retention: Loses 5%, keeps 95% = 0.95 per day.
  2. Formula: C(t)=100(0.95)tC(t) = 100(0.95)^t.
  3. Test:
    • Day 4: 100(0.95)481.45%100(0.95)^4 \approx 81.45\% (above 80%)
    • Day 5: 100(0.95)577.38%100(0.95)^5 \approx 77.38\% (below 80%) ✓
  4. Answer: 5 days.

💡 Strategic Tip: Test successive days to find when it crosses the threshold.

Choice B is incorrect because charge is still above 80% at day 4. Choice C is incorrect because charge is well above 80% at day 3. Choice D is incorrect because it drops below 80% before day 6.