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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 ...
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 wheat and chessboard problem (sometimes expressed in terms of rice grains) is a mathematical problem expressed in textual form as: If a chessboard were to have wheat placed upon each square such that one grain were placed on the first square, two on the second, four on the third, and so on (doubling the number of grains on each subsequent ...
The growth constant k is the frequency (number of times per unit time) of growing by a factor e; in finance it is also called the logarithmic return, continuously compounded return, or force of interest. The e-folding time τ is the time it takes to grow by a factor e. The doubling time T is the time it takes to double.
The doubling time (t d) of a population is the time required for the population to grow to twice its size. [24] We can calculate the doubling time of a geometric population using the equation: N t = λ t N 0 by exploiting our knowledge of the fact that the population (N) is twice its size (2N) after the doubling time. [20]
t = time. The model can also be written in the form of a differential equation: = with initial condition: P(0)= P 0. This model is often referred to as the exponential law. [5] It is widely regarded in the field of population ecology as the first principle of population dynamics, [6] with Malthus as the founder.