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A mathematical problem of calculating the number of grains of wheat on a chessboard if each square has twice as many grains as the previous one. Learn about its origins, solutions, and applications in exponential growth, compound interest, and technology strategy.
Exponential growth is a process that increases quantity over time at an ever-increasing rate. It occurs when the rate of change is proportional to the quantity itself. See examples, formula, and applications in biology, physics, economics, finance, and computer science.
Find formulas for indefinite and definite integrals of exponential functions and their combinations. Learn how to use error function, exponential integral, and other ...
The Leslie matrix is a discrete, age-structured model of population growth that is widely used in population ecology. It describes the survival and fecundity of individuals in different age classes and calculates the asymptotic growth rate and stable age distribution of the population.
Learn how organisms can grow exponentially when resources are unlimited, and how this growth is affected by competition and carrying capacity. See examples, equations, graphs and references for biological exponential growth.
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation , where is the carrying capacity, the logistic growth rate, and is the value of the function. Learn about the history, applications, symmetries, inverse, derivative, integral, and differential equation of the logistic function.
Learn about the rapid growth of the complexity of a problem due to the way its combinatorics depends on input, constraints and bounds. See examples of combinatorial explosion in mathematics, puzzles, games, computing and arithmetic.
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.
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