# DBT JRF 2022 — Question 97

Exam: DBT JRF 2022 · Section: B · Topic: Bioprocess Engineering › Fed-Batch Reactor - Exponential Feed · Difficulty: Medium

## Question

An exponentially increasing feed of concentrated substrate is fed into a fed batch reactor to maintain a constant specific growth rate 0.35
$$h^{-1}$$
 . If the feed is 5 ml/hr at time, t = 0, then feed after 4 hrs will be approximately:

## Options

- **A.** 5 ml/hr
- **B.** 10 ml/hr
- **C.** 20 ml/hr
- **D.** 80 ml/hr

## Answer

Option C

## Explanation

Exponential feeding in fed-batch fermentation: In fed-batch culture with exponential feeding: $F(t) = F_0 \cdot e^{\mu t}$ where $F_0$ is initial feed rate, $\mu$ is the desired specific growth rate, t is time. Given: $F_0 = 5\,\text{mL/hr}$ , $\mu = 0.35\,\text{h}^{-1}$ , $t = 4\,\text{h}$ : $F(4) = 5 \times e^{0.35 \times 4} = 5 \times e^{1.4}$ $e^{1.4} \approx 4.055$ $F(4) = 5 \times 4.055 \approx 20.3\,\text{mL/hr} \approx 20\,\text{mL/hr}$ Answer: Feed rate at t = 4 h $\approx 20\,\text{mL/hr}$ .

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