## Exponential Growth

If they were able to grow freely without outside constraints (and no removal or death), cells growing by binary fission would follow the pattern depicted in Figure 11.18. Under these conditions the time between each successive split, producing a new

Figure 11.18 Theoretical microbial growth schematic.

"generation" of daughter cells, is constant and is called the generation time (tg). Since the number of cells doubles each generation, the same period also is commonly referred to as the doubling time (td). This type of growth pattern is referred to as exponential growth. Note that whereas the time period is constant, the number of new cells added during that period doubles each time.

Most people do not have an intuitive feeling for exponential growth. As a simple mental exercise, picture folding a standard sheet of paper in half, then in half again, and again. Imagine that you could continue folding it in half 50 times. How tall would the folded stack of paper then be: a meter? 100 m a football field)? New York to San Francisco (^5000 km)? After first trying to guess, calculate an approximate answer by assuming that the paper is 0.1 mm thick and doubles each time it is folded (or 0.1 mm x 250). (Note: 210 = -103.)

Minimum Doubling Times Under ideal growth conditions, microorganisms will achieve their most rapid growth and hence their minimum td. This value is inherent to the particular strain of organism (for the system in which it is growing), and there is in fact a tremendous range of minimum doubling times in the microbial world. Some examples are shown in Figure 11.19.

Many common fast-growing bacteria (e.g., Escherichia coli) can have generation times of only 20 minutes. A few, such as the thermophile Bacillus stearothermophilus (found, for example, in composting piles), grow even more rapidly, with minimum generation times of around 10 minutes. This is about 1,000,000 times faster than a typical human generation of approximately two decades!

Prokaryotes in general have faster growth rates than eukaryotes, with their greater complexity. However, there are also slow-growing bacteria. Organisms tend to adapt to

Monilinia fructicola Saccharomyces cerevisiae

Giardia lamblia Leishmania donovani Paramecium caudatum Tetrahymena geleii

Ceratium tripos Euglena gracilis Asterionella formosa Scenedesmus quadricauda

Nitrobacter wiinogradsky Anabaena cylindrica Rhodospirullum rubrum Clostridium botulinum Bacillus subtilis Escherichia coli