The Number e definitions Flashcards
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.
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