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How to be a king
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Maths Portfolio
Population Growth
Population growth is an extremely relevant study considering its boom in recent centuries and consequently the problems that this may cause on resources. It has therefore become imperative to develop means by which population sizes can be predicted into the future. This can achieved through mathematical modeling whereby a function is attached to a population growth curve.
The purpose of this investigation is to create such a function from the population growth curve of England and Wales from 1801 to 151.
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NB Although most populations follow a relatively sequential and predictable growth, the fact that population growth is a biological process means that mathematical modeling will never be a perfect means of predicting future populations. Erratic abiotic factors can disrupt normal growth in a capricious and unpredictable manner. Nevertheless, modeling does offer a useful, albeit limited means of looking into the future from our observations of the past and at the moment it is our only means of doing so.
Population Growth Curve for England and Wales 1801-151 (fig 1.0)
The curve follows a growth pattern similar to exponential growth from 1801 to 111. At this point there is a noticeable drop in growth which largely falls away from the expected growth of the curve. Growth for 111 to 151 is largely constant.
Since
Population growth = birth rate death rate
The sudden change in concavity from 111 onwards could be due to the extremely high death rate during World War One. This very drastically upset the growing but balance between these two variables from 1801 to 111. During WWI a very high death rate destroyed this steady growth reducing the difference and consequently resulting in a much lower growth rate for this time period. When modeling this curve the prevalent growth rate before 111 can be taken with an adjustment for the change during 111 to 11. Also, the time period 141 to 151 also experienced a war further disrupting the growth. The sudden change can further be expressed in figures
Furthermore an average per year can be taken clearly illustrating the sudden change in growth.
Although this is a very superficial calculation it clearly demonstrates the change in growth. Also, this calculation works on the assumption that growth is constant which is not necessarily true as the curve is in fact exponential.
Total Population change from 1801 to 151 = 48655 people
Average population change = 46 people per annum
Average Growth Rate
Average growth rate This is the increase in population per annum
This equation ultimately is exactly the same as the equation for gradient
as population rises on the y-axis and time on the x-axis.
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