Q58 E. coli is inoculated in a shake flask containing nutrient medium. The initial number of viable cells in the medium is 10². After few hours, the number of viable cells is 10⁶. Assuming cell divides by binary fission, the number of generations that have taken place is ______ (rounded off to the nearest integer).

The number of generations for E. coli cells growing from 10² to 10⁶ viable cells via binary fission is 13

Growth Formula

Bacterial populations double per generation during binary fission, following:

N = N₀ × 2ⁿ

where N is the final cell count, N₀ is the initial count, and n is generations.

Here, N₀ = 10² = 100 and N = 10⁶ = 1,000,000, so:

2ⁿ = 10⁶ / 10² = 10⁴

Solving yields:

n = log₂(10⁴) = 4 log₂(10) ≈ 13.29, rounded to 13.

Step-by-Step Calculation

Rearrange to:

n = log₂(N) − log₂(N₀) = log₂(N / N₀)

log₂(10) ≈ 3.321928, so:

4 × 3.321928 = 13.287712

Nearest integer rounding (13.287712 → 13) matches standard practice.

Introduction to E. coli Generations Calculation Binary Fission

In microbiology, E. coli generations calculation binary fission determines growth doublings in shake flask experiments, vital for competitive exams like IIT JAM. Starting with 10² viable cells reaching 10⁶ assumes exponential log phase without lag or death.

Binary Fission Mechanism

E. coli divides by binary fission, doubling cells per generation: 1 → 2 → 4 → 8 (2ⁿ). Viable cells track live counts post-inoculation in nutrient medium.

Exact Calculation Steps

Use N = N₀ × 2ⁿ, so 2ⁿ = 10⁴.

Then n = 4 log₂(10); log₂(10) = ln(10)/ln(2) ≈ 3.3219.

Result: 13.2877, rounded to 13.

Common Exam Pitfalls

• 4 (ignores base-2)
• 20 (misuses log10)
• 13.3 (no rounding)

Binary fission excludes multi-fission; shake flask implies ideal conditions.

Application in IIT JAM Prep

Practice E. coli shake flask growth for biotech/microbiology sections; verify with:

n = log₂(N / N₀)