1
advanced-math

A blockchain network's hashrate grows as H(t)=100e0.12tH(t) = 100e^{0.12t} exahashes/s where tt is months. When does it reach 1,000 exahashes/s?

A

About 19.2 months

B

About 25 months

C

About 15 months

D

About 30 months

Correct Answer: A

Choice A is the correct answer. Solve for tt when H(t)=1000H(t) = 1000.

  1. Equation: 1000=100e0.12t1000 = 100e^{0.12t}.
  2. Divide: 10=e0.12t10 = e^{0.12t}.
  3. Natural log: ln(10)=0.12t\ln(10) = 0.12t.
  4. Solve: t=ln(10)0.12=2.3030.1219.1919.2t = \frac{\ln(10)}{0.12} = \frac{2.303}{0.12} \approx 19.19 \approx 19.2 months.

💡 Strategic Tip: Memorize ln(10)2.303\ln(10) \approx 2.303 for quick calculations.

Choice B is incorrect because this is too long. Choice C is incorrect because this is too short. Choice D is incorrect because this is way too long.