Escherichia coli doubles every 20 minutes starting from 100 cells, reaching 13,107,200 cells after 17 generations. The logarithmic number (base-10 log) of cells at this point is 7.1.

Calculation Method

Bacterial growth follows exponential doubling via binary fission, where each generation multiplies the cell count by 2. The formula is N = N₀ × 2ⁿ, with N₀ = 100 (initial cells) and n = 17 (generations). Substituting gives
N = 100 × 2¹⁷ = 100 × 131072 = 13,107,200 cells.

The logarithmic number means log₁₀(N). Compute log₁₀(13,107,200) = log₁₀(100) + log₁₀(2¹⁷) = 2 + 17 × log₁₀(2) ≈ 2 + 17 × 0.3010 = 7.117, rounded to 7.1.

Step-by-Step Generations

Track key milestones to verify:

Each step confirms doubling every generation under the 20-minute condition.

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Introduction

Escherichia coli growing under favorable conditions doubles every 20 minutes, a key concept in microbial growth for CSIR NET life sciences. Starting with 100 initial Escherichia coli cells, find the logarithmic number of cells at the 17th generation (up to 1 decimal place). This exponential growth problem uses N = N₀ × 2ⁿ and log₁₀ for precise calculation.

Understanding Exponential Growth in E. coli

E. coli exhibits logarithmic phase growth via binary fission, doubling populations predictably. With a 20-minute generation time, 17 generations span 17 × 20 = 340 minutes. Initial 100 cells yield 2¹⁷ = 131,072 doublings, totaling 13,107,200 cells.

Detailed Log Calculation

Apply log₁₀(N) = log₁₀(100 × 2¹⁷) = 2 + 17 log₁₀(2). Since log₁₀(2) ≈ 0.3010, 17 × 0.3010 = 5.117, so 2 + 5.117 = 7.117 ≈ 7.1. This matches bacterial growth formulas in textbooks.

CSIR NET Exam Tips

• Practice similar problems: generation time confirms rapid E. coli proliferation despite DNA replication overlaps.
• Verify with Python: confirms 7.1 exactly.
• Common errors include natural log or forgetting base-10 specification.