As you probably know the two largest countries in the world

As you probably know, the two largest countries in the world in terms of population are China and India. At the beginning of the year 2011, China\'s population was estimated at 1.36 billion with an annual growth rate of .47% while India\'s population that same year was estimated around 1.21 billion with an annual growth rate of 1.41%. Build a continuous growth equation setting China\'s population model equal to that of India\'s and use your algebraic skills to estimate the year (nearest 10^th) in which India would potentially surpass China in population. Make a rough sketch to illustrate your mathematics and use your calculator to check for reasonableness.

Solution

Population can be modellled :

P = Po(1 +i)^x

i = growth rate

x = no. of years sinc 2011

China: P = 1.36(1+0.0047)^x = 1.36(1.0047)^x

India : P = 1.21(1+0.0141)^x = 1.21(1.0141)^x

Equating the two equations:

1.36(1.0047)^x =1.21(1.0141)^x

(1.0141/1.0047)^x = 1.36/1.21 = 1.1239

1.009^x = 1.1239

taking log on both sides:

xln(1.009) = ln(1.1239)

x = 13.03 =13 years

In the year 2024 India would surpass the popoulation of China