Exponential growth doubling time

Exponential growth occurs after cell metabolisms have adjusted and before a key nutrient becomes limiting or toxic products accumulate. In the exponential growth phase, the total cell mass will increase by a fixed percentage during each time interval, typically doubling every few hours. Ultimately, however, the... 

The average time required for a cell to perform an entire cell cycle successively is defined as the cell cycle time (Tc), that in asynchronous cells and without quiescent fraction can be approximate to doubling time, calculated from exponential cell growth. 

Escherichia coli grows with a doubling time of 0.5 h in the exponential growth phase. 

Evaluate the doubling time during the exponential growth phase. 

Put another way, during exponential growth the microbial population will double in number for every time interval, t = (In 2)1 fx. 

The exponential growth rate constant k is equal to the number of doublings per unit time. Thus, k is the reciprocal of the doubling time. It is easy to show that the number of bacteria present at time t will be given by the following equation. 

When contamination occurs, the microorganisms start to adapt to the new environmental conditions. This initial slow or no-growth period is called the lag phase, and the shelf life of a food item is directly proportional to the length of this phase (Fig. 4—40). The adaptation period is followed by an exponential growth period during which the population of microorganisms can double two or more times every hour under favorable conditions unless drastic sanitation measures are taken. The depletion of nutrients and the accumulation of toxins slow down the growth and start the death period. 

For those readers more interested in this thought process, it is the reverse of population growth and doubling times. It is actually the mathematics of exponentials, but I promised to leave mathematics out of this book. Anyone who can divide by 2 or multiply by one-half can easily calculate these exposures. 

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