5
advanced-math

A new cryptocurrency gains value at 15% per week. If it's worth $0.50 now, when will it reach $1.00?

A

Between 4 and 5 weeks

B

7 weeks

C

10 weeks

D

2 weeks

Correct Answer: A

Choice A is the correct answer. Find when value doubles.

  1. Formula: V(t)=0.50(1.15)tV(t) = 0.50(1.15)^t, solve for 1.00=0.50(1.15)t1.00 = 0.50(1.15)^t.
  2. Simplify: (1.15)t=2(1.15)^t = 2.
  3. Test:
    • t=4t=4: (1.15)41.749(1.15)^4 \approx 1.749 (below 2)
    • t=5t=5: (1.15)52.011(1.15)^5 \approx 2.011 (above 2) ✓
  4. Answer: Between 4 and 5 weeks.

💡 Strategic Tip: Rule of 72 gives rough estimate: 72154.8\frac{72}{15} \approx 4.8 weeks.

Choice B is incorrect because doubling happens sooner. Choice C is incorrect because growth is much faster. Choice D is incorrect because(1.15)21.32eq2(1.15)^2 \approx 1.32 eq 2.