The doubling time for Escherichia coli is 20 minutes, and you start getting sick when just 10 bacteria enter your system. How many bacteria are in your body after 12 hours?

Understanding doubling time is key to comprehending bacterial growth. Doubling time refers to the period it takes for a population to double in size. For Escherichia coli, or E. coli, this period is remarkably short at just 20 minutes. This means that under optimal conditions, E. coli can double every 20 minutes. Regularly breaking up microbial populations into periods makes predicting their growth more manageable.

For example, if we start with 10 bacteria and give it 20 minutes, we will have 20 bacteria. After another 20 minutes, we will have 40, and so on.

Understanding and calculating doubling time is essential in fields like microbiology and epidemiology, where predicting the speed of bacterial spread or infection rates is crucial.

Bacterial populations, including E. coli, typically grow exponentially under ideal conditions. Exponential growth means that the population size increases at a rate proportional to the current size.

The formula for exponential growth can be written as: \[ N = N_0 \times 2^n \] where:
- \( N \) is the final number of bacteria.
- \( N_0 \) is the initial number of bacteria.
- \( n \) is the number of doubling intervals.

This kind of growth results in very rapid increases in population size over relatively short periods. For instance, with the doubling time of 20 minutes, a single bacterial cell of E. coli can result in billions of cells in just a matter of hours.

Let's break down the bacterial growth calculation using the example problem step by step.

First, convert the total time into units compatible with the doubling time. In our exercise, we convert 12 hours into minutes, which gives us 720 minutes.

Next, determine how many doubling intervals fit into those 720 minutes. Since the doubling time is 20 minutes, we divide 720 by 20, resulting in 36 doubling intervals.

Finally, use the exponential growth formula: \[ N = 10 \times 2^{36} \] Here, our initial population (\( N_0 \)) is 10 bacteria, and we have 36 doubling intervals (\( n \)). Solving this, we find \( N = 6.87 \times 10^{10} \), which means after 12 hours, there are approximately 68.7 billion bacteria. This high value illustrates the speed at which bacteria can grow under ideal conditions.

Escherichia coli, commonly known as E. coli, is a type of bacteria found in the intestines of humans and animals. Most strains are harmless and play a vital role in digestion. However, some strains can cause food poisoning and other serious health problems.

E. coli is frequently used in research due to its well-understood genetics and ability to grow rapidly. This makes it a model organism in biotechnology and microbiology.

Due to its short doubling time of 20 minutes, E. coli can proliferate very quickly under optimal conditions, making it essential to understand its growth patterns, especially for public health and medical fields. This rapid growth is beneficial in laboratory research but can pose significant risks if uncontrolled in natural or clinical settings.