exponential

Meanings

• noun

  A mathematical function where the value of the function at any input is the base value raised to the power of that input. For example, in the function f(x) = 2^x, the value of f(2) is 2^2 = 4.

  - "The population of a certain species increases exponentially."
  - "The interest earned on an investment grows exponentially."
  - "Exponential growth is characterized by a constant percentage increase."

• noun

  In computer science, a method of calculating the value of a function where the value of the function at any given input is the base value raised to the power of the input.

  - "The algorithm uses an exponential search method to find the desired value."
  - "The recursive function exhibits exponential time complexity."
  - "The exponential growth of data requires efficient storage solutions."

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Pronunciation

1. /ˌɛk.spoʊ.ˈnɛn.tʃəl/
   
   
   
   Source: "https://commons.wikimedia.org/w/index.php?curid=10618508"

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Rhymes

Words rhyming with exponential
expansional , revolving , devolving , evolving

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Variants

List of all variants of exponential that leads to same result
exponential , exponentially , exponential function , exponential functions

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Etymology

origin and the way in which meanings have changed throughout history.

Derived from the Latin word 'exponere', meaning 'to expose' or 'to explain'. In mathematics, 'exponential' refers to the power or exponent, and the function that represents this relationship.

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Trivia

Any details, considerations, events or pieces of information regarding the word

1. The concept of exponential growth was first studied by mathematicians in the 17th century.

2. Exponential growth is a common phenomenon in nature, such as the growth of populations of certain species.

3. Exponential growth is often used to model the spread of diseases, as well as the growth of financial markets and technological innovation.

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Related Concepts

informations on related concepts or terms closely associated with the word. Discuss semantic fields or domains that the word belongs to

1. Logarithm: Logarithms are the inverse functions of exponential functions. While exponential functions represent the power of a base raised to a power, logarithmic functions represent the power to which the base must be raised to obtain a given value.

2. Exponential growth rate: The exponential growth rate is a measure of the percentage increase in the value of a function over a given time period. It is calculated as the natural logarithm of the final value divided by the natural logarithm of the initial value, multiplied by 100 to obtain a percentage.

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Culture

Any cultural, historical, or symbolic significance of the word. Explore how the word has been used in literature, art, music, or other forms of expression.

Exponential growth is a common theme in various fields of science, economics, and technology. It has been studied extensively in mathematics and physics, and its applications range from population growth to financial markets to technological innovation.

How to Memorize "exponential"

1. visualize
   

   - To memorize the concept of exponential growth, imagine a balloon being inflated. The size of the balloon increases exponentially with each puff of air.

2. associate
   

   - Associate the word 'exponential' with the concept of 'growth'. This can help you remember that exponential functions represent functions where the value increases at a constant percentage rate.

3. mnemonics
   

   - Use the mnemonic 'Elephants Eat Leaves Every Year' to remember the formula for exponential growth: F(t) = F0 * (b ^ t). Replace 'Elephants' with 'Exponential', 'Leaves' with 'Ln' for natural logarithm, 'Every' with 'E', and 'Year' with 't'.

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