7
advanced-math

E. coli bacteria double every 20 minutes. Starting with 100 cells, how many after 2 hours?

A

6,400 cells

B

1,200 cells

C

800 cells

D

3,200 cells

Correct Answer: A

Choice A is the correct answer. Calculate doublings over 2 hours.

  1. Periods: 2 hours = 120 minutes, so 12020=6\frac{120}{20} = 6 doublings.
  2. Formula: N(t)=100(2)t/20N(t) = 100(2)^{t/20} where t=120t = 120 minutes.
  3. Calculate: N(120)=100(2)6=100(64)=6,400N(120) = 100(2)^6 = 100(64) = 6,400.

💡 Strategic Tip: 6 doublings = multiply by 26=642^6 = 64.

Choice B is incorrect because this assumes linear growth. Choice C is incorrect because this is after only 3 doublings. Choice D is incorrect because this is after 5 doublings.