Introduction

Bacteria grow by binary fission, where each cell divides into two.
This leads to exponential growth.
The number of times the population doubles is called the
generation number (n).
In this problem, we calculate the generations per hour.

Given Data

Initial population (N₀) = 10³

Final population (N) = 10⁹

Time (t) = 10 hours

Find: Generations per hour

Growth Formula

Bacterial growth equation:

N = N₀ × 2ⁿ

where:

• N = final population
• N₀ = initial population
• n = number of generations

Step-by-Step Solution

Step 1: Substitute values

10⁹ = 10³ × 2ⁿ

Step 2: Simplify

10⁹ / 10³ = 2ⁿ

10⁶ = 2ⁿ

Step 3: Take logarithm

n = log(10⁶) / log 2

n = 6 / 0.301 ≈ 20

Step 4: Generations per hour

Generations per hour = n / t

= 20 / 10 = 2

Final Answer

2 generations per hour

Correct Option: (D)

Explanation of All Options

• (A) 20 – Total generations, not per hour
• (B) 10 – Incorrect division
• (C) 4 – Calculation mistake
• (D) 2 – Correct value (20 ÷ 10)

Important Exam Formulas

n = (log N − log N₀) / log 2

Generations per hour = n / t

Shortcut: 10⁶ ≈ 2²⁰

Conceptual Understanding

Each generation doubles the population.
Higher generations per hour indicate faster bacterial growth.
This concept is widely used in fermentation technology and microbiology.