how do you calculate the population growth?
According to census results, the population of India was 846.3 million 1991 and 1.027 billion (1,027 million) in 2001.
(a) Estimate the current (2009) population of India.
(b) Predict the year that India's population will surpass 1.5 billion.
- 1 decade agoFavorite Answer
population growth is exponential and can be expressed as a function of time. Let P = population, then:
P = Ae^kt where t = time in years and A and k are constants which we need to calculate from your data.
Firstly lets start in 1991 when time = 0, so
P = Ae^k*0 = A so A = 846.3 million
P = 846.3*e^kt
Now lets work out k - we do this by using the second piece of data - 2001 is ten years after 1991 so let t=10. - the population in 2001 is 1027 million so
1027 = 846.3e^10k
e^10k = 1.21...
10k = ln 1.21...
k = 0.0194 to 3d.ps
So our final formula is:
P = 846.3e^0.0194t [Check this using your data to make sure]
Now using this formula you can solve the actual questions!
1. 2009 - 1991 = 18 so sub in t= 18
P= 846.3e^(0.0194*18) = 1200million
2. Again we need to find t and we need P = 1500
15000 = 846.3e^0.0194t
17.72... = e^0.0194t
ln(17.71)/0.0194 = 148.1 round up to 149. So 1991 + 149 = 2140. So it will surpass 1.5billion in 2140.
Hope that helps!
- 1 decade ago
I think you should use the Compound Annual Growth Rate (CAGR) formula, something like this: http://www.investopedia.com/terms/c/cagr.asp. (you are assuming that the yearly growth rate will remain the same during the time period.)
For the question (b): After getting the CAGR, then just multiply (e.g. grow) 1.027 by the CAGR for each year until you go beyond 1.5. For example, if your CAGR is .08, then
2002: 1.027 x 1.08 = 1.10916
2003: 1.10916 x 1.08 and so on.