Population Growth - Geometric Progression - Essay Example

Download file to see previous pages Geometric series has been multiplied by a factor of 4, this kind of progression or growth is sometimes called exponential growth to means something that grows very fast (Galan, Luard, and Mazzucchelli, 65). Geometric growth can be contrasted to arithmetic growth rate, which grows in a sequence, for instance, 1, 5, 9, 13, 17, 21, 25, 29, 33, 37,...  One of the principles behind geometric growth is that the bigger a number gets, the faster it grows, this is the case with population since the larger the population becomes, more people will be available for reproduction hence the greater growth (Berlatsky, 133). For instance, a population having 500,000 people will grow five times faster than a population which has just 100, 000. To calculate geometric growth for the population in a given time, the following formula can be used.  Assume population x depends exponentially on time t, then      x(t) = a.bt/r    where a is the initial value of the population meaning that    x.0 = a,    b is a constant growth factor and r is the time that is required for a population to increase by a unit factor of b, therefore;   x(t +r) = a.bt+r/r =  a.bt/r + br/r =    x(t).b   From this equation, if r is greater than zero and b is greater than one, then the population will grow exponentially, however, if r is less than zero and b is greater than one or if r is greater than one and b is between one and zero, then the population will reduce exponentially. A geometric decay curve for the population would look something like this Example The initial population of a city is 100, 000 people, It is believed that the population doubles every five years, find the population after 20 years and plot it in a graph. Solution      x(t) = a.bt/r  x(20) = 100, 000 · 220/5 = 100, 000 · 24 = 100, 000 · 16 = 1, 600, 000 Therefore the population after 20 years will be 1, 600, 000 people In a graph   Geometric (continuous growth) model The geometric continuous time model of population growth is more realistic when it comes to determining population growth since they involve all parameters of the population such as birth rates and death rate (Turchin, p96) To calculate the population growth rate using the continuous growth model, the following formula can be derived. If a population has Nt individuals where t is time in years, the number of children being born in a year is a fraction represented by the symbol  and the number of people that die in a year is a fraction that is represented by the symbol .   Solving this equation further would give the following final equation   These geometric progression equations have been used for a long time to calculate population growth rates of countries or the world at large, for instance, the following figure shows a curve of world growth rate that was calculated from the available data and backward projections of population.

Geometric progression has been used in population growth and without it, calculating projections on growth rates would be very difficult, tThereason, why it has been used in calculating population growth, is because the population grows at an exponential rate with a certain factor from the initial population. Several formulas can be derived for calculating population growth rate depending on whether they are discrete or continuous models, however, continuous models are the most appropriate since they are more realistic.  ...Download file to see next pages Read More