Exponential growth

Exponential growth is change in which a quantity’s rate of increase is proportional to its current size. Under a constant growth rate, the quantity grows by equal proportions over equal time intervals.

Exponential function: A function in which the variable appears in the exponent, such as f(x) = a·bˣ. Its curve describes quantities that change by equal proportions over equal intervals.
Population growth: Change in the number of individuals in a population over time. A population can grow exponentially when each individual contributes a constant average number of new individuals.
Proportionality: A relationship in which one quantity varies as a constant multiple of another. Exponential growth begins with a rate proportional to the amount already present.
Linear growth: Growth by equal absolute amounts over equal intervals of time. Unlike exponential growth, its increase per interval does not scale with the current quantity.
Differential equation: An equation relating an unknown function to one or more of its derivatives. The equation dN/dt = rN states the defining rate relationship for continuous exponential growth.
Bacterial growth: An increase in bacterial cell numbers, often through repeated cell division. In favorable conditions, repeated division produces near-exponential increases.
Rate of change: The amount by which a quantity changes per unit change in another variable. Growth is exponential specifically when the rate of change tracks the current quantity.
Polynomial growth: Growth described by a power of the independent variable, such as a quadratic function. It can accelerate over time but does not maintain a constant proportional rate.
Doubling time: The time required for a growing quantity to become twice its initial size. A constant proportional growth rate gives a constant doubling time.
Pandemic: An epidemic that spreads across multiple countries or continents. Early epidemic spread can be approximately exponential when transmission opportunities remain plentiful.

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