EXPONENTIAL GROWTH Meaning and
Definition
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Exponential growth refers to a rapid and continuous increase or expansion in quantity over time, where the rate of increase is proportional to the current value. In this type of growth, the higher the current value, the greater the amount of growth that occurs. As a result, the growth rate itself accelerates as the quantity of interest gets larger.
In mathematical terms, exponential growth is often represented by an exponential function, which can be expressed as y = a * (1 + r)^t. Here, "y" denotes the final quantity, "a" represents the initial amount, "r" stands for the growth rate per time period, and "t" denotes the number of time periods.
Exponential growth can be observed in various contexts, such as the growth of populations, financial investments, or the spread of diseases. For example, when a population experiences exponential growth, it means that the number of individuals rapidly multiplies over time. Similarly, in finance, investments that generate exponential growth would continuously and increasingly accumulate wealth.
However, it is important to note that exponential growth is not sustainable in the long run since resources and environmental factors ultimately limit growth. As the quantity being measured reaches its carrying capacity or maximum sustainable level, the growth rate begins to slow down and may eventually stabilize or decline.
Common Misspellings for EXPONENTIAL GROWTH
- wxponential growth
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- 4xponential growth
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Etymology of EXPONENTIAL GROWTH
The word "exponential" originates from the Latin word "exponere", which means "to set forth" or "to explain". The term "growth" is derived from the Old Norse word "grōa" which means "to grow" or "to thrive". In the context of mathematics and science, the term "exponential growth" refers to a rapid and continuous increase in quantity over time, where the rate of growth is proportional to the current value. The concept was first introduced and utilized formally in mathematics by the Swiss mathematician Jacob Bernoulli in the late 17th century.
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