Search results
Results from the WOW.Com Content Network
For example, with an annual growth rate of 4.8% the doubling time is 14.78 years, and a doubling time of 10 years corresponds to a growth rate between 7% and 7.5% (actually about 7.18%). When applied to the constant growth in consumption of a resource, the total amount consumed in one doubling period equals the total amount consumed in all ...
For example, in microbiology, a population of cells undergoing exponential growth by mitosis replaces each cell by two daughter cells, so that = and is the population doubling time. If the population grows with exponential growth rate r {\displaystyle \textstyle r} , so the population size at time t {\displaystyle t} is given by
Many pairs (b, τ) of a dimensionless non-negative number b and an amount of time τ (a physical quantity which can be expressed as the product of a number of units and a unit of time) represent the same growth rate, with τ proportional to log b. For any fixed b not equal to 1 (e.g. e or 2), the growth rate is given by the non-zero time τ.
The formula above can be used for more than calculating the doubling time. If one wants to know the tripling time, for example, replace the constant 2 in the numerator with 3. As another example, if one wants to know the number of periods it takes for the initial value to rise by 50%, replace the constant 2 with 1.5.
The large impact of a relatively small growth rate over a long period of time is due to the power of exponential growth. The rule of 72, a mathematical result, states that if something grows at the rate of x% per year, then its level will double every 72/x years. For example, a growth rate of 2.5% per annum leads to a doubling of the GDP within ...
RGR is a concept relevant in cases where the increase in a state variable over time is proportional to the value of that state variable at the beginning of a time period. In terms of differential equations , if S {\displaystyle S} is the current size, and d S d t {\displaystyle {\frac {dS}{dt}}} its growth rate, then relative growth rate is
Compounding growth over multiple periods. For example, if a company achieves 30% growth in one year, but its results remain unchanged over the two subsequent years, this would not be the same as 10% growth in each of three years. CAGR, the compound annual growth rate, addresses this issue. [1]
r = the population growth rate, which Ronald Fisher called the Malthusian parameter of population growth in The Genetical Theory of Natural Selection, [2] and Alfred J. Lotka called the intrinsic rate of increase, [3] [4] t = time. The model can also be written in the form of a differential equation: =