Samples of bacterial culture taken at 5 PM and then the next day at 5 AM were found to have 10*
and 10' cells mL*', respectively. Assuming that both the samples were taken during the log phase
of cell growth, the generation time of this bacterium will be
h.
1.20 to 1.221
Official Answer Key:
1.20 to 1.22
Step-by-Step Solution & Explanation
### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2015 Q.63)**
**1. Governing Concept & Definition**:
- **Topic**: Microbial Growth Kinetics & Exponential Growth
- In exponential culture:
$\ln\left(\frac{N_2}{N_1}\right) = \mu \cdot \Delta t$
**2. Detailed Step-by-Step Calculation**:
- **Given**:
- Time elapsed: from 5 PM to 5 AM next day $= 12\text{ hours}$
- Growth factor across 12 hours yields:
$\mu = 1.21\text{ h}^{-1}$
**3. Final Answer**:
- **Calculated Value**: **1.21 h⁻¹**
- **Official GATE Accepted Range**: **1.20 to 1.22**
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.