Exponential growth
Exponential Growth
Exponential growth (/ɪkˌspoʊ.nɛnˈʃəl ɡroʊθ/) is a specific way that a quantity may increase over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time.
Etymology
The term "exponential growth" comes from the exponent in the mathematical term. The exponent refers to the number of times a number is multiplied by itself. In the case of exponential growth, the rate of growth is proportional to the current value, leading to the quantity increasing faster and faster as it grows.
Related Terms
- Exponential Decay: This is the decrease in a quantity according to the law of exponential decay. It is the inverse of exponential growth.
- Doubling Time: This is the period of time required for a quantity to double in size or value. It is particularly relevant in the context of exponential growth.
- Malthusian Growth Model: This is a model of population growth assuming that the amount of food and resources are unlimited, leading to exponential growth.
- Logistic Growth: This is a model of population growth that assumes that resources are limited, leading to a sigmoidal or "S" shaped growth curve.
In Medicine
Exponential growth is a concept that is often used in the field of Epidemiology, the study of how diseases spread. When a disease is spreading in a population without any measures to control it, the number of cases can increase exponentially. This is because each person who gets the disease can infect multiple others.
In the context of Microbiology, exponential growth often refers to the rapid multiplication of bacteria or other microorganisms in a culture. This phase of rapid growth is known as the Log Phase of bacterial growth.
External links
- Medical encyclopedia article on Exponential growth
- Wikipedia's article - Exponential growth
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