6
advanced-math

Moore's Law states that computing power doubles every 2 years. If a processor has power P0P_0 in 2020, what is its power in 2030?

A

32P032P_0

B

16P016P_0

C

10P010P_0

D

64P064P_0

Correct Answer: A

Choice A is the correct answer. Calculate the number of doubling periods.

  1. Time elapsed: 2030 - 2020 = 10 years.
  2. Doubling periods: 102=5\frac{10}{2} = 5 periods.
  3. Formula: P(t)=P0(2)t/2P(t) = P_0(2)^{t/2}.
  4. Calculate: P(10)=P0(2)5=P0(32)=32P0P(10) = P_0(2)^5 = P_0(32) = 32P_0.

💡 Strategic Tip:nn doublings = multiply by 2n2^n.

Choice B is incorrect because this is 242^4 (only 4 doublings). Choice C is incorrect because this assumes linear growth. Choice D is incorrect because this is 262^6 (6 doublings).