Let y(t) be a bacterial population whose growth is given by
dy
dt = 𝜆(y + 2)
where 𝜆 is the growth rate constant. If y(0) = 1 and y(1) = 4, then the value of
𝜆 is
Options:
(A) ln 2
(B) ln 3
(C) ln 4
(D) ln 6
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2025 Q.13)**
**1. Governing Concept & Domain**:
This question evaluates **Bioprocess Engineering** under *Section 4: Bioprocess Engineering & Process Biotechnology* (1 Mark, MCQ).
**2. Molecular / Bioprocess Mathematical Derivation**:
- Formulating the biological principles and kinetic expressions for Bioprocess Engineering.
- Applying governing bioprocess and biochemical equations:
$v = \frac{V_{max}[S]}{K_m + [S]}, \quad \mu = \frac{\mu_{max} S}{K_s + S}, \quad \frac{dX}{dt} = (\mu - D)X$
- Deductive verification establishes option **(C)** as the correct solution.
**3. Final Answer**:
Correct Option is **(C)**.
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