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The Number e definitions

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  • Exponential Function
    A mathematical expression where a constant base is raised to a variable exponent, often modeling rapid growth or decay.
  • Base e
    A mathematical constant approximately 2.71828, used as the base in natural exponential functions and linked to continuous growth.
  • Pi
    A mathematical constant representing the ratio of a circle's circumference to its diameter, approximately 3.14159.
  • Natural Exponential Function
    A function of the form f(x) = e^x, where e is the mathematical constant for continuous growth or decay.
  • Continuous Compounding
    A process where interest is added an infinite number of times per period, leading to the mathematical constant e.
  • Limit
    A value that a function or sequence approaches as the input or index approaches some value, often infinity.
  • Transformation
    A change applied to a function's graph, such as shifting, stretching, or reflecting, without altering its basic shape.
  • Population Growth
    An application of exponential functions, often modeled using base e, to describe how populations increase over time.
  • Radioactive Decay
    A process modeled by exponential functions with base e, describing how unstable substances decrease over time.
  • Half-life
    The time required for a quantity to reduce to half its initial value, commonly modeled with exponential decay.
  • Calculator
    A device or tool used to evaluate expressions, including those involving e, often using the 'second ln' function for exponents.
  • Exponent
    A mathematical notation indicating the number of times a base is multiplied by itself.
  • Compounding Interest
    A financial concept where interest is calculated on both the initial principal and accumulated interest, leading to exponential growth.
  • Graph
    A visual representation of a function, showing the relationship between variables, such as f(x) = e^x.
  • Decimal Representation
    A way of expressing numbers using digits and a decimal point, as seen in the non-terminating expansion of e.