# DBT JRF 2020 — Question 16

Exam: DBT JRF 2020 · Section: B · Topic: Microbiology · Difficulty: Medium

## Question

Consider a bacterium that grows with doubling time of 20 min in the exponential phase of its growth cycle and acquire 10 random mutations in its genome in every generation. How many mutations will it acquire after 48 hr of growth in exponential phase?

## Options

- **A.** 1404
- **B.** 1044
- **C.** 1440
- **D.** 1000

## Answer

Option C

## Explanation

In a constant-volume fed-batch culture (substrate fed at constant rate $F$ with feed concentration $S_f$ ): The substrate balance is $\dfrac{d(VS)}{dt} = FS_f - \mu X V / Y_{X/S}$ . As culture proceeds, cell biomass $X$ increases (more cells competing for the same substrate feed rate). With fixed $F$ and $S_f$ , the substrate concentration per cell decreases. From Monod kinetics: $\mu = \dfrac{\mu_{\max} S}{K_s + S}$ — as $S$ decreases (because substrate is consumed faster by the growing biomass), $\mu$ decreases. Declining $\mu$ with increasing biomass is the hallmark of non-exponential growth in fed-batch cultures.

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