GATE 2026 BT – Question 55
A microbial culture (following Monod model for growth) has a maximum specific growth rate of 0.1 h$^{-1}$, Monod constant of 1 mg L$^{-1}$ and endogenous decay rate of 0.1 day$^{-1}$. At limiting substrate concentration of 23 g L$^{-1}$, the net specific growth rate will be ________day$^{-1}$. (rounded off to one decimal place)
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Correct answer: 2.29 to 2.31
Explanation
The maximum rate is $0.1 \times 24 = 2.4$ day$^{-1}$. With $S = 23000$ mg/L $\gg K_s = 1$ mg/L, $\mu = 2.4\times\frac{23000}{23001} \approx 2.4$. The net rate is $\mu - k_d = 2.4 - 0.1 = 2.3$ day$^{-1}$.