The Number e definitions Flashcards
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.
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