# The Final Number of Bacterial Cells

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This Demonstration allows students to graphically explore the final number of bacterial cells that result when bacteria are placed in favorable, unrestrained cell-growth conditions for multiple reproductive cycles (generations). The basic formula applied is: .

Contributed by: Todd D. Allen (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

This Demonstration provides students with a graphical interpretation of bacterial (or generally, any microbial) cell growth that is in exponential growth phase.

Snapshot 1: an absolute scale plot of bacterial cell numbers resulting from an initial starting population of 35 cells, proceeding through 17 rounds of binary fission

Snapshot 2: the same conditions as in Snapshot 1, except now plotted on a logarithmic scale

Snapshot 3: A single cell allowed to double through 25 rounds of binary fission can produce a population size of 33,554,432 cells! (If the time between generations is 30 minutes, this population size would be achieved in 12.5 hours!)

The interested microbiology student should quickly notice two useful features of plotting cell numbers on a log scale:

1. Bacterial growth, as plotted logarithmically, generates a straight line. This indicates that the percent change from one generation to the next is constant.

2. In the absence of adaptive plotting software (such as *Mathematica*), cell numbers expressed in logarithms make it much easier to plot the entire spectrum of growth curve data (both small and very large absolute cell numbers) on the same piece of graph paper, as is traditionally done in the lab setting.

For further information exploring the mathematical treatment of microbial growth, the reader is referred to any introductory text in microbiology, including:

G. J. Tortora, B. R. Funke, and C. L. Case, *Microbiology: An Introduction*, 9th ed., San Francisco: Benjamin Cummings, 2007.

## Permanent Citation

"The Final Number of Bacterial Cells"

http://demonstrations.wolfram.com/TheFinalNumberOfBacterialCells/

Wolfram Demonstrations Project

Published: March 7 2011