Q.80 During a bacterial growth experiment, the total viable cell count at
2 h and 6 h was
1 × 104 cells/ml and
1 × 109 cells/ml, respectively.
The specific growth rate (in h−1) of the culture is
____________________.
Introduction
The specific growth rate (μ) is an important parameter in microbiology and biotechnology.
It represents the rate of increase in microbial biomass per unit time during the exponential
(log) phase of growth.
Given Data
- Viable cell count at 2 h = 1 × 104 cells/ml
- Viable cell count at 6 h = 1 × 109 cells/ml
Formula Used
μ = (ln N2 − ln N1) / (t2 − t1)
Step-by-Step Calculation
Step 1: Identify Values
- N1 = 1 × 104 cells/ml
- N2 = 1 × 109 cells/ml
- t1 = 2 h
- t2 = 6 h
Time interval = 6 − 2 = 4 h
Step 2: Substitute Values
μ = [ln(109) − ln(104)] / 4
μ = ln(105) / 4
Step 3: Final Calculation
ln(105) = 5 × 2.303 = 11.515
μ = 11.515 / 4 = 2.88 h−1
Final Answer:
Specific growth rate (μ) = 2.88 h−1
Specific growth rate (μ) = 2.88 h−1
Conclusion
The calculated specific growth rate indicates rapid bacterial multiplication,
which is characteristic of cells growing in the exponential phase.
