The Number e definitions Flashcards
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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.