The World Population 1

Fugo Takasu
takasu@es.nara-wu.ac.jp
Department of Chemistry, Biology and Environmental Science
Nara Women’s Unviersity, Nara, Japan

3 July 2017

How many people live on the earth now?

We connect to the Wolfram database to obtain the data of the world population.

CountryData["World","Population"]

The Wolfram database is a bit outdated. The world population has been estimated 7.3 billion in 2015 (US Census Buerau: http://www.census.gov/popclock/).

data=CountryData["World",{"Population",All}]

The data is available from 1970 to 2013.

DateListPlot[data,PlotMarkers->Automatic]

How large was the world popoulation in 1970, 1980, 1990, 2000, and 2010?

data1=CountryData["World",{"Population",1970}]

data2=CountryData["World",{"Population",1980}]

ratioIncrease=(data2-data1)/data1

The world population increased by 20.5 % from 1970 to 1980.

1+ratioIncrease

The world population grew in size 1.20 times larger from 1970 to 1980.

(1+ratioIncrease)^(1/10)

Averaged annual increase was 1.88 % in 10 years from 1970 to 1980.

How large was the annual increase rate of the world population in the decade from 1980, 1990, and 2000?

The world population has been increasing. We are curious to know how it will grow in size in future.

Why should we concern the world population or the demography of human being in future?

Country by country population size

Choose a country and examine its population size now and in the past.

CountryData[]

dataJapan=CountryData["Japan",{"Population",All}]

DateListPlot[dataJapan,PlotMarkers->Automatic]

DateListPlot[dataJapan,PlotMarkers->Automatic,PlotRange->{{DateList["1900"],DateList["2015"]},All}]

CountryData["Japan","Shape"]

CountryData["World","Shape"]

CountryData["EastAsia","Shape"]

CountryData["EastAsia"]

GeoListPlot[{LinguisticAssistant,LinguisticAssistant,LinguisticAssistant,LinguisticAssistant,LinguisticAssistant,LinguisticAssistant,LinguisticAssistant}]

Exponential growth

Let (Subscript[N, t]) be the population size in year t. If the population increases by r % every year, then the population size in the next year t + 1 is given as
	
	(Subscript[N, t+1])= (1 + r / 100) (Subscript[N, t])

This is a geometric series and one the inital population size is give, the solution is easily obtained.

	(Subscript[N, t])=(Subscript[N, 0])(r^t)

Numerical example

nextPopSize[x_]:=(1+r/100)x/.r->1.8

seq=NestList[nextPopSize,1,100]

ListPlot[seq,Joined->True,AxesLabel->{"Year","Pop size"}]

ListLogPlot[seq,Joined->True,AxesLabel->{"Year","Pop size"}]

Exponential growth becomes a straight line when plotted in logarithmic scale.

Doubling time

In an exponential growth, how long does it take for the population size to be doubled?

Log[2]/Log[1+r/100]/.r->1.8