GATE BT 2024 • Q34
NAT • 1 Mark
Section 2: General Biotechnology
Microbial growth kinetics
Subtopic: Fundamentals of Microbial growth kinetics
Question Statement:
If the rate at which E. coli divides is 0.5 h-1, then its doubling time is ________ h.
Official Answer Key:
2 to 2
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2024 Q.34)**
**1. Governing Concept & Definition**:
- **Topic**: Microbial Growth Kinetics & Generation Time
- **Division Rate ($v$) vs Doubling Time ($t_d$)**: In bacterial exponential cell division, the division rate constant $v$ is the number of generations per unit time ($v = 1 / t_d$).
**2. Detailed Step-by-Step Calculation**:
- **Given**: Rate at which *E. coli* divides = $0.5 ext{ h}^{-1}$.
- **Formula**:
$t_d = rac{1}{v}$
- **Substitution**:
$t_d = rac{1}{0.5 ext{ h}^{-1}} = 2.0 ext{ h}$
**3. Final Answer**:
- **Calculated Value**: **2**
- **Official GATE Accepted Range**: **2 to 2**
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