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Exponential Meaning: Definition, Examples, and Translations

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exponential

[ˌɛkspəˈnɛnʃəl ]

Definitions

Context #1 | Adjective

mathematics growth

Exponential refers to a mathematical function where a quantity increases by a constant factor over equal intervals. It is often used to describe rapid growth, especially in contexts like population increase, technology adoption, and finance.

Synonyms

accelerated, increase, rapid.

Examples of usage

  • The population is experiencing exponential growth.
  • The technology market is expanding exponentially.
  • The bacteria multiplied at an exponential rate.
Context #2 | Noun

mathematical function

In mathematics, an exponential is a type of function where a variable appears in the exponent. It is typically expressed in the form f(x) = a * b^x, where b is a positive real number.

Synonyms

exponent, power.

Examples of usage

  • The graph of the exponential function shows a steep curve.
  • In calculus, we study the properties of exponential functions.
  • An exponential model can be used to fit the data.

Translations

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Interesting Facts

Science

  • Exponential growth is commonly seen in populations of organisms where resources are unlimited, like bacteria in a petri dish.
  • Many natural phenomena, like the spread of diseases or viral videos online, can grow exponentially when certain conditions are met.
  • In physics, exponential decay describes processes such as radioactive decay, where substances lose their quantity at a rate proportional to their current value.

Mathematics

  • In mathematics, exponential functions are crucial for modeling real-world situations, such as finance (interest on investments).
  • The graph of an exponential function has a characteristic 'J' shape, demonstrating how outputs increase rapidly.
  • Exponential equations often involve a constant base raised to a variable exponent, showing how small changes in the exponent lead to significant changes in value.

Technology

  • The rapid expansion of technology and data storage can be described as exponential growth, leading to advancements like artificial intelligence.
  • The concept is fundamental in the field of computer science, especially with algorithms that improve efficiency at an exponential rate.
  • The term 'Moore's Law' refers to the observation that the number of transistors on a microchip doubles approximately every two years, demonstrating exponential progress in computing power.

Economics

  • In finance, compound interest leads to exponential growth of investments over time, highlighting the power of investing early.
  • Economic theories often describe systems that can grow exponentially, particularly in capitalist economies with unrestricted growth potential.
  • Exponential trends can lead to predictions about future wealth or market behaviors, showing both opportunities and risks.

Origin of 'exponential'

Main points about word origin

  • The term comes from the Latin word 'exponere', meaning 'to set forth', indicating how it illustrates changes in size.
  • It became widely used in mathematics by the 19th century, particularly in calculus and functions relating to growth.
  • The symbol for exponential growth is the letter 'e' raised to a power, representing the base of natural logarithms.

The term 'exponential' comes from the Latin word 'exponere', which means 'to set forth'. The mathematical use of the term began in the 16th century when it was used to denote powers in equations. The adjective form emerged later to describe functions that grow at rates proportional to their current value. In the context of mathematics, it plays a crucial role in concepts such as compound interest, population dynamics, and various scientific models. Exponential growth has become a fundamental concept in understanding phenomena that exhibit rapid increases, making it a common term across multiple disciplines.

Word Frequency Rank

Position #9,100 indicates this is an advanced-level word. While not essential for basic communication, it will enhance your ability to understand and create more nuanced content.