# DBT JRF 2022 — Question 23

Exam: DBT JRF 2022 · Section: A · Topic: Microbiology › Bacterial Growth Kinetics · Difficulty: Medium

## Question

A growing bacterial culture doubles in 1 hr; the increase in cell mass in 30 minutes will be:

## Options

- **A.** Zero
- **B.** 50%
- **C.** Less than 50%
- **D.** More than 50%

## Answer

Option C

## Explanation

Exponential bacterial growth — increase in 30 minutes: For exponential (log-phase) growth with doubling time $T_d = 1$ hour: Cell mass at time t: $N(t) = N_0 \times 2^{t/T_d}$ At $t = 30$ min = 0.5 h: $N(0.5) = N_0 \times 2^{0.5} = N_0 \times \sqrt{2} \approx 1.414\,N_0$ Percentage increase = $(\sqrt{2} - 1) \times 100\% \approx 41.4\%$ Since 41.4% < 50%, the increase is LESS THAN 50%. Intuition: In linear growth, 30 min = half the doubling time = 50% increase. But in EXPONENTIAL growth, growth accelerates over time — the first half of the doubling period adds less than the second half. Hence the increase is less than 50%. Answer: Less than 50% (Option 3).

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