Calculation of Generation Time

Problem: If one starts with 100,000 (10⁵) cells in a culture that has a generation time of 2 h, how many cells will be in the culture after 8, 16, and 32 h?

Use the equation:

X = 2ⁿ X₀

where X₀ is the initial number of cells, n is the number of generations, and X is the number of cells after n generations.

After 8 hours

n = 8 h / 2 h per generation = 4 generations

X = 2⁴ × 10⁵ = 6.554 × 10⁶ cells

After 16 hours

n = 16 h / 2 h per generation = 8 generations

X = 2⁸ × 10⁵ = 2.56 × 10⁷ cells

After 32 hours

n = 32 h / 2 h per generation = 16 generations

X = 2¹⁶ × 10⁵ = 6.554 × 10¹¹ cells

Reference

1. Pepper, I. L., Gerba, C. P., & Brendecke, J. W. (2009). Environmental Microbiology: A Laboratory Manual (2nd ed.). Elsevier. ISBN 9780123705198