vækstraten

Vækstraten, the Danish term for growth rate, is the rate at which a quantity increases or decreases over time. It is commonly expressed as a percentage per time unit and is used across disciplines such as economics, demography, and biology. The term can refer to various specific growth rates, including the growth rate of real GDP, the population growth rate, or the growth rate of a biological population.

Mathematically, the discrete growth rate over a time interval Δt is r = (Q_t - Q_0)/Q_0, often reported as a percentage per year. The continuously compounded growth rate g is defined as g = (1/Q) dQ/dt, and the solution to dQ/dt = g Q is Q(t) = Q(0) e^{g t}. In many practical contexts, growth rates are annualized or expressed per other chosen time units.

Interpretation: if r > 0 or g > 0, the quantity increases; if negative, it declines. Growth rates can be affected by base effects, seasonality, and structural changes. Data limitations, measurement error, and the choice of time unit can influence observed rates.

Applications and limitations: Growth rates are used in forecasting and policy analysis, including economic planning, population projections, and biological studies. Limitations include volatility, regime shifts, and the possibility that a constant growth rate is unrealistic over long horizons; rates can mask underlying dynamics such as logistic growth.

See also: compound growth, exponential growth, GDP growth rate, population growth rate, logistic growth, demography.