5
advanced-math

An endangered species population triples every 10 years. If there are now 150 individuals, how many will there be in 30 years?

A

4,050

B

1,350

C

450

D

13,500

Correct Answer: A

Choice A is the correct answer. Apply the tripling pattern.

  1. Periods: 3010=3\frac{30}{10} = 3 periods of tripling.
  2. Formula: P(t)=150(3)t/10P(t) = 150(3)^{t/10} where t=30t = 30.
  3. Calculate: P(30)=150(3)3=150(27)=4,050P(30) = 150(3)^3 = 150(27) = 4,050.

💡 Strategic Tip: 3 triplings = multiply by 33=273^3 = 27.

Choice B is incorrect because this is after 2 triplings (20 years). Choice C is incorrect because this is after only 1 tripling (10 years). Choice D is incorrect because this would be after 4 triplings.