7
advanced-math

A smartphone app has 10,000 users. Users increase by 30% each month. When will it reach 100,000 users?

A

Between 8 and 9 months

B

12 months

C

6 months

D

10 months

Correct Answer: A

Choice A is the correct answer. Find when users reach 100,000.

  1. Formula: U(t)=10000(1.30)tU(t) = 10000(1.30)^t, solve for 100000=10000(1.30)t100000 = 10000(1.30)^t.
  2. Simplify: (1.30)t=10(1.30)^t = 10.
  3. Test:
    • t=8t=8: (1.30)88.157(1.30)^8 \approx 8.157 (below 10)
    • t=9t=9: (1.30)910.604(1.30)^9 \approx 10.604 (above 10) ✓
  4. Answer: Between 8 and 9 months.

💡 Strategic Tip: Test integer values to bracket the answer.

Choice B is incorrect because growth happens faster. Choice C is incorrect because(1.30)64.83(1.30)^6 \approx 4.83. Choice D is incorrect because it exceeds 100,000 before month 10.