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The Number e definitions

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  • E
    A mathematical constant approximately 2.71828, serving as the base for natural exponential functions and arising from continuous compounding.
  • Exponential Function
    A mathematical expression where a constant base is raised to a variable exponent, often modeling rapid growth or decay.
  • Base
    The fixed number in an exponential expression that is raised to a power, such as 2, 3, or e.
  • Exponent
    The variable or number indicating how many times the base is multiplied by itself in an exponential expression.
  • Pi
    A mathematical constant approximately 3.1415, often compared to e due to its non-repeating decimal nature.
  • Second Ln Function
    A calculator feature used to compute values of e raised to a given power, typically accessed by pressing '2nd' then 'ln'.
  • Graph
    A visual representation of a function, showing the relationship between input values and their corresponding outputs.
  • Transformation
    A method for altering the position or shape of a graph, such as shifting, stretching, or reflecting.
  • Compounding Interest
    A financial process where interest is calculated on both the initial principal and accumulated interest, leading to exponential growth.
  • Population Growth
    A real-world phenomenon often modeled by exponential functions, describing how populations increase over time.
  • Radioactive Decay
    A process where unstable substances decrease in quantity over time, commonly modeled using exponential functions with base e.
  • Half-life
    The time required for a quantity to reduce to half its initial value, frequently associated with exponential decay.
  • Continuous Compounding
    A scenario where interest is added an infinite number of times per period, resulting in growth described by the constant e.
  • Natural Exponential Function
    A function with base e, commonly written as f(x) = e^x, modeling continuous growth or decay.
  • Decimal Expansion
    The non-terminating, non-repeating sequence of digits representing numbers like e and pi.