Logarithm and bacteria

Medical tests often require the enumeration of bacteria, viruses, or other organisms to determine the progress of a disease or the effectiveness of a medication.

Logarithm and bacteria

Bring fact-checked results to the top of your browser search. Growth of bacterial populations Growth of bacterial cultures is defined as an increase in the number of bacteria in a population rather than in the size of individual cells.

The growth of a bacterial population occurs in a geometric or exponential manner: The time required for the formation of a generation, the generation time Gcan be calculated from the following formula: Bacteria can be pathogenic disease-causing and may produce toxins that can spoil foods Logarithm and bacteria cause food poisoning.

Some diseases caused by bacteria include botulism, typhoid fever, and pneumonia. In the formula, B is the number of bacteria present at the start of the observation, b is the number present after the time period t, and n is the number of generations.

The relationship shows that the mean generation time is constant and that the rate at which the number of bacteria increases is proportional to the number of bacteria at any given time. This relationship is valid only during the Logarithm and bacteria when the population is increasing in an exponential manner, called the log phase of growth.

For this reason, graphs that show the growth of bacterial cultures are plotted as the logarithm of the number of cells.

Book Launch: Atomic Habits

The generation time, which varies among bacteria, is controlled by many environmental conditions and by the nature of the bacterial species.

For example, Clostridium perfringensone of the fastest-growing bacteria, has an optimum generation time of about 10 minutes; Escherichia coli can double every 20 minutes; and the slow-growing Mycobacterium tuberculosis has a generation time in the range of 12 to 16 hours.

The composition of the growth medium is a major factor controlling the growth rate. The growth rate increases up to a maximum when the medium provides a better energy source and more of the biosynthetic intermediates that the cell would otherwise have to make for itself.

Generalized bacterial growth curve showing the phases in the growth of bacterial colonies. Bacterial colonies progress through four phases of growth: When bacteria are placed in a medium that provides all of the nutrients that are necessary for their growth, the population exhibits four phases of growth that are representative of a typical bacterial growth curve.

Upon inoculation into the new medium, bacteria do not immediately reproduce, and the population size remains constant.

During this period, called the lag phasethe cells are metabolically active and increase only in cell size. They are also synthesizing the enzymes and factors needed for cell division and population growth under their new environmental conditions. The population then enters the log phasein which cell numbers increase in a logarithmic fashion, and each cell generation occurs in the same time interval as the preceding ones, resulting in a balanced increase in the constituents of each cell.

The log phase continues until nutrients are depleted or toxic products accumulate, at which time the cell growth rate slows, and some cells may begin to die. Under optimum conditions, the maximum population for some bacterial species at the end of the log phase can reach a density of 10 to 30 billion cells per millilitre.

Logarithm and bacteria

The log phase of bacterial growth is followed by the stationary phasein which the size of a population of bacteria remains constant, even though some cells continue to divide and others begin to die.

The stationary phase is followed by the death phase, in which the death of cells in the population exceeds the formation of new cells. The length of time before the onset of the death phase depends on the species and the medium.In mathematics, logarithmic growth describes a phenomenon whose size or cost can be described as a logarithm function of some input.

e.g. y = C log (x).

Logarithm and bacteria

Note that any logarithm base can be used, since one can be converted to another by multiplying by a fixed constant. [1]. Nov 13,  · The predominant observable in this context was a bacteria count or density. The notable finding was that one could take the logarithm of this count, divide it by time, and obtain a growth parameter that was nearly constant.

The Meaning of Enumerate Gets Specific.

This site is no longer maintained and has been left for archival purposes

In a census year, the U.S. government attempts to enumerate every single citizen of the country—a task that, even in the modern era of technology, isn't truly possible. "Log reduction" is a mathematical term (as is "log increase") used to show the relative number of live microbes eliminated from a surface by disinfecting or cleaning.

For example, a "5-log reduction". The technical definition of pH is that it is a measure of the activity of the hydrogen ion (H+) and is reported as the reciprocal of the logarithm of the hydrogen ion activity.

Figure E. Changes in temperature (solid line) and populations of mesophilic fungi (broken line) and thermophilic fungi (dotted line) in a wheat straw kaja-net.com on data in Chang & Hudson, The left axis shows fungal populations (logarithm of colony forming units per gram of compost plated onto agar); the right axis shows temperature in the centre of the compost.

Exponential and logarthmic functions | Khan Academy