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GATE 2022 ES – Question 38

Environmental Microbiology · Growth and Control of Microorganisms · 2 marks · Multiple choice

For exponential microbial growth with specific rate μ, find doubling time t_d.

  1. t_d=μ
  2. t_d=μ²
  3. $t_d=\ln2/\mu$
  4. $t_d=\frac12\ln\mu$

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Correct answer: (C) $t_d=\ln2/\mu$

Explanation

Exponential growth is $X=X_0e^{\mu t}$. At doubling,2=e^{μt_d}; taking natural logarithms gives $t_d=\ln2/\mu$, **C**. The reciprocal-rate dependence also supplies the correct unit of time.

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