Exponential: meaning, definitions and examples

Etymology

• 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.

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.

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.

• ...
• 9097 evolve
• 9098 grease
• 9099 journalism
• 9100 exponential
• 9101 remanded
• 9102 enrichment
• 9103 weeping
• ...