10
advanced-math

A phone's battery percentage follows B(t)=100(0.92)tB(t) = 100(0.92)^t where tt is hours. After how many hours is the battery at 50%?

A

Between 8 and 9 hours

B

Exactly 50 hours

C

Between 2 and 3 hours

D

After 10 hours

Correct Answer: A

Choice A is the correct answer. Solve 100(0.92)t=50100(0.92)^t = 50.

  1. Simplify: (0.92)t=0.5(0.92)^t = 0.5.
  2. Test Values:
    • t=8t=8: (0.92)80.51(0.92)^8 \approx 0.51 (above 0.5)
    • t=9t=9: (0.92)90.47(0.92)^9 \approx 0.47 (below 0.5)
  3. Conclusion: Answer is between 8 and 9 hours.

💡 Strategic Tip: For SAT, estimation and testing values is often faster than logarithms.

Choice B is incorrect because 50 is the target percentage, not the time. Choice C is incorrect because the decay is too slow for this short time. Choice D is incorrect because by hour 10, battery would be below 50%.