3
advanced-math

A tree's height increases by 8% each year. If currently 10 feet tall, when will it reach 15 feet?

A

Between 5 and 6 years

B

10 years

C

3 years

D

8 years

Correct Answer: A

Choice A is the correct answer. Find when height reaches 15 feet.

  1. Formula: H(t)=10(1.08)tH(t) = 10(1.08)^t, solve for 15=10(1.08)t15 = 10(1.08)^t.
  2. Simplify: (1.08)t=1.5(1.08)^t = 1.5.
  3. Test:
    • t=5t=5: (1.08)51.469(1.08)^5 \approx 1.469 (below 1.5)
    • t=6t=6: (1.08)61.587(1.08)^6 \approx 1.587 (above 1.5)
  4. Answer: Between 5 and 6 years.

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

Choice B is incorrect because growth happens much faster. Choice C is incorrect because(1.08)31.26<1.5(1.08)^3 \approx 1.26 < 1.5. Choice D is incorrect because it reaches 15 feet before year 8.