7
advanced-math

A population starts at 1,000 and doubles every year. After how many years will the population first exceed 8,000 based on the table?

YearPopulation
01,000
12,000
24,000
38,000
A

3 years

B

4 years

C

2 years

D

5 years

Correct Answer: B

Choice B is the correct answer. The table shows populations at each year mark.

  1. Check Table: At year 3, population = 8,000 (equals, not exceeds).
  2. Pattern: Population doubles: P(t)=1000(2)tP(t) = 1000(2)^t.
  3. Year 4: P(4)=1000(2)4=16,000>8,000P(4) = 1000(2)^4 = 16,000 > 8,000.
  4. Conclusion: First exceeds 8,000 at year 4.

💡 Strategic Tip: "Exceed" means strictly greater than, not equal to.

Choice A is incorrect because at year 3, the population equals 8,000, not exceeds. Choice C is incorrect because at year 2, population is only 4,000. Choice D is incorrect because the population exceeds 8,000 before year 5.