9
advanced-math

An EV battery's capacity degrades to 80% of original after 1,000 charge cycles. What is the decay factor per cycle?

A

About 0.9998

B

About 0.99

C

About 0.9995

D

About 0.98

Correct Answer: A

Choice A is the correct answer. Find the decay factor per cycle.

  1. Model: C(n)=C0bnC(n) = C_0 b^n where bb is decay factor per cycle.
  2. After 1000 cycles: 0.80C0=C0b10000.80C_0 = C_0 b^{1000}.
  3. Simplify: 0.80=b10000.80 = b^{1000}.
  4. Solve: b=(0.80)1/1000=0.800.001b = (0.80)^{1/1000} = 0.80^{0.001}.
  5. Calculate: b0.9998b \approx 0.9998 (loses about 0.02% per cycle).

💡 Strategic Tip: Small decay per cycle compounds to significant loss over many cycles.

Choice B is incorrect because this loses 1% per cycle (too much). Choice C is incorrect because this loses 0.05% per cycle. Choice D is incorrect because this loses 2% per cycle (way too much).