Exponential function

A function in which the variable appears in the exponent, commonly written as f(x) = aˣ for a positive base a not equal to 1. Its rate of change is proportional to its value.

Natural exponential function: The exponential function with base e, written eˣ; it is its own derivative. Its derivative equals itself, making it the central exponential in calculus.
Exponentiation: The operation of raising a number to a power. An exponential function places its input in the exponent of a fixed base.
Compound interest: Interest calculated on both an initial principal and previously accumulated interest. Repeated compounding produces exponential growth in the account balance.
Polynomial function: A function formed from a finite sum of constant multiples of nonnegative integer powers of its input. Here the variable is raised to fixed powers, rather than serving as an exponent.
John Napier: A Scottish mathematician who introduced logarithms in the early seventeenth century. His logarithms made calculations involving exponential relationships more manageable.
Exponential growth: A process whose rate of increase is proportional to its current amount. A positive exponential function models growth at a constant proportional rate.
Exponent: A number that indicates how many times a base is used as a factor, extended to other powers. The input of an exponential function occupies this position.
Radioactive decay: The spontaneous transformation of unstable atomic nuclei, with a constant probability per unit time for each nucleus. The expected number of undecayed nuclei follows exponential decay.
Linear function: A function whose graph is a straight line, commonly written f(x) = mx + b. Its constant additive rate of change differs from exponential proportional change.
Leonhard Euler: An eighteenth-century Swiss mathematician who established notation and results central to modern analysis. His work helped make e and the natural exponential function central mathematical objects.

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