9
advanced-math

A bacteria culture triples every 2 hours. Starting with 500 bacteria, how many are there after 8 hours?

A

40,500

B

13,500

C

4,500

D

1,500

Correct Answer: A

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

  1. Tripling periods: 82=4\frac{8}{2} = 4 periods.
  2. Formula: N(t)=500(3)t/2N(t) = 500(3)^{t/2} where t=8t = 8.
  3. Calculate: N(8)=500(3)4=500(81)=40,500N(8) = 500(3)^4 = 500(81) = 40,500.

💡 Strategic Tip: 4 triplings = multiply by 34=813^4 = 81.

Choice B is incorrect because this is after 3 triplings (6 hours). Choice C is incorrect because this is after 2 triplings (4 hours). Choice D is incorrect because this is after only 1 tripling (2 hours).

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Set 31: Exponential Functions 31