Search results
Results from the WOW.Com Content Network
In the long run, exponential growth of any kind will overtake linear growth of any kind (that is the basis of the Malthusian catastrophe) as well as any polynomial growth, that is, for all α: = There is a whole hierarchy of conceivable growth rates that are slower than exponential and faster than linear (in the long run).
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 ...
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 is the current size, and its growth rate, then relative growth rate is =. If the RGR is constant, i.e., =, a solution to this equation is
Rutherford applied the principle of a radioactive element's half-life in studies of age determination of rocks by measuring the decay period of radium to lead-206. Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation. The accompanying table shows the ...
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: =
Therefore, the thermodynamic entropy, which is proportional to the marginal entropy, must also increase with time [8] (note that "not too long" in this context is relative to the time needed, in a classical version of the system, for it to pass through all its possible microstates—a time that can be roughly estimated as , where is the time ...
A large number of fundamental equations in physics involve first or second time derivatives of quantities. Many other fundamental quantities in science are time derivatives of one another: force is the time derivative of momentum; power is the time derivative of energy; electric current is the time derivative of electric charge; and so on.
In physics, sometimes units of measurement in which c = 1 are used to simplify equations. Time in a "moving" reference frame is shown to run more slowly than in a "stationary" one by the following relation (which can be derived by the Lorentz transformation by putting ∆x′ = 0, ∆τ = ∆t′):