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Exponential decay is a process where a quantity decreases at a rate proportional to its current value. Learn the differential equation, the decay constant, the mean lifetime, the half-life, and the applications of exponential decay in physics, chemistry, biology, and more.
In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form y = a x k {\displaystyle y=ax^{k}} – appear as straight lines in a log–log graph, with the exponent corresponding to ...
Half-life is the time required for a quantity to reduce to half of its initial value, commonly used in nuclear physics to describe radioactive decay. Learn how half-life depends on the reaction order, the decay constant and the initial concentration, and see examples of different decay processes.
Exponential growth is a process that increases quantity over time at an ever-increasing rate. Learn the formula, the graph, and the applications of exponential growth in biology, physics, economics, finance, computer science, and internet phenomena.
The birth–death process (or birth-and-death process) is a special case of continuous-time Markov process where the state transitions are of only two types: "births", which increase the state variable by one and "deaths", which decrease the state by one.
Learn about the exponential function, a mathematical function that relates the rate of change to the value of the function. See how it is defined, graphed, and extended to complex numbers and matrices, and how it relates to logarithms and trigonometric functions.
Doubling time is the time it takes for a population to double in size or value. Learn how to calculate it from the growth rate, and see examples of doubling times for various phenomena such as population, inflation, interest and tumours.
Residence time is the total time that a fluid parcel spends inside a control volume, such as a reactor, a lake, or a human body. Learn about the residence time distribution, the mean residence time, the turnover time, and the simple flow models of different reactors.