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GATE 2024 BT – Question 58

Fundamentals of Biological Engineering · Bioreaction Engineering: Kinetics of cell growth, substrate utilization and product formation, structured and unstructured models · 2 marks · Numerical answer

E. coli is inoculated in a shake flask containing nutrient rich medium. The initial number of viable cells in the medium is $10^2$. After few hours, the number of viable cells is $10^6$. Assuming cell divides by binary fission, the number of generations that have taken place is ________ (rounded off to the nearest integer).

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Correct answer: 13

Explanation

$10^6 = 10^2 \times 2^n$, so $2^n = 10^4$ and $n = \frac{4}{\log 2} = 13.3 \approx 13$.