10

Set 13: Exponential Functions (Advanced)

Explanation

Answer: A

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

A.

5 days

✓ Correct
B.

4 days

C.

3 days

D.

6 days

Detailed Explanation

Choice A is correct. 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.

Key Steps:

The correct answer is 5 days

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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