GATE 2021 ES – Question 34

Environmental Microbiology · Growth and Control of Microorganisms · 1 mark · Numerical answer

A culture grows from 5×10⁴ to 1280×10⁴ cells/mL by binary fission with no deaths. Find number of generations as an integer.

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Correct answer: 8 to 8

Explanation

Population ratio is 1280/5=256=2⁸. Binary fission multiplies population by 2 per generation, so $n=\log_2(N/N_0)=8$. Therefore **8 generations**. The common10⁴ factor cancels.

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