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The exponential time-constant for the process is =, so the half-life is (). The same equations can be applied to the dual of current in an inductor. Furthermore, the particular case of a capacitor or inductor changing through several parallel resistors makes an interesting example of multiple decay processes, with each resistor representing ...
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential (or, rarely ...
The problem may be solved using simple addition. With 64 squares on a chessboard, if the number of grains doubles on successive squares, then the sum of grains on all 64 squares is: 1 + 2 + 4 + 8 + ... and so forth for the 64 squares. The total number of grains can be shown to be 2 64 −1 or 18,446,744,073,709,551,615 (eighteen quintillion ...
In mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear differential equations with spatially varying coefficients. It is typically used for a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and ...
Application. Half-exponential functions are used in computational complexity theory for growth rates "intermediate" between polynomial and exponential. [ 2] A function grows at least as quickly as some half-exponential function (its composition with itself grows exponentially) if it is non-decreasing and , for every .[ 5]
The functional square root of the exponential function (now known as a half-exponential function) was studied by Hellmuth Kneser in 1950. [1]The solutions of f(f(x)) = x over (the involutions of the real numbers) were first studied by Charles Babbage in 1815, and this equation is called Babbage's functional equation. [2]
For example, logarithms are used to solve for the half-life, decay constant, or unknown time in exponential decay problems. They are important in many branches of mathematics and scientific disciplines, and are used to solve problems involving compound interest .
Technetium-99m. The first technetium-99m generator, 1958. A 99m Tc pertechnetate solution is being eluted from 99 Mo molybdate bound to a chromatographic substrate. Technetium-99m (99m Tc) is a metastable nuclear isomer of technetium-99 (itself an isotope of technetium), symbolized as 99m Tc, that is used in tens of millions of medical ...