116. 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:
A. 5 ml/hr
B. 10 ml/hr
C. 20 ml/hr
D. 80 ml/hr

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Detailed Explanation:

Fed-batch reactors are widely used in biotechnology to maintain optimal conditions for cell growth by gradually feeding nutrients. When a constant specific growth rate (μ) is desired, an exponential feeding strategy is employed.

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Given:

• Initial feed rate at $t=0$: F0=5 ml/hrF_0 = 5 \, \text{ml/hr}F0=5ml/hr

• Specific growth rate: μ=0.35 hr−1\mu = 0.35 \, \text{hr}^{-1}μ=0.35hr−1

• Time $t=4\text{hrs}$

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Formula for Exponential Feed Rate:

F(t)=F0⋅eμtF(t) = F_0 \cdot e^{\mu t}F(t)=F0⋅eμt

Substitute values:

F(4)=5⋅e0.35⋅4=5⋅e1.4F(4) = 5 \cdot e^{0.35 \cdot 4} = 5 \cdot e^{1.4}F(4)=5⋅e0.35⋅4=5⋅e1.4

Now calculate:

e1.4≈4e^{1.4} \approx 4e1.4≈4 $$F(4)\approx 5\cdot 4=20\text{ml/hr}$$

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Final Answer:

C. 20 ml/hr

This feed strategy is essential for maintaining a steady state of cell growth while preventing substrate inhibition and overflow metabolism, especially in industrial-scale fermentations.