Population Growth Calculation

[ISENBERG]

For every country I have a birthrate "X". Wikipedia says to divide 70 by "X" to get # of years to double the population.

Unfortunately, that's not the question or answer I need. Given "X" and the current population "Y," I want to know what the population will be in 6 years.

I can find current population "Y" for each country by checking Wikipedia. I just don't know whether the method I need to get future population after "Z" years uses algebra, calculus, or statistics. Worse, I never took any courses in either calculus or statistics. The means I need clear instructions on what I need to do to get the answer.

I've just written my first novel, and only then did I realize that I had used current populations for each nation. I want this novel to be accurate to the best of my ability, and am not satisfied with the answer "No one will ever notice."

Thank you for your answer or reference to a different Board on this site.

Edward D. Isenberg
Author@FederationOfPeoples.com

 

[tkhunny]

70? Usually, it's 72. This is only a rugh approximation and is a decent approximation only for a small range of values. You need logarithms or exponents.

If you have an annual growth rate, r = 4% = 0.04.
If you have c current population, P = 2,000,000
The population in six years is P*(1+r)^6 = 2,000,000(1.04)^6 = 2,000,000*1.265319018496 = 2530638.036992

You WILL have to decide two things:

1) What will I do with the fractions? Normally, if you are just interested in the total population, simply discard them. 2,530,638
2) Can the population REALLY continue to grow at that rate? In the Azores, for example, you would have a bit of trouble growing indefinitely, since they are rather small and only so many people actually would fit!

 

[ISENBERG]

What will I do with the fractions? Normally, if you are just interested in the total population, simply discard them. 2,530,638

Fractions are not only easy to ignore, but for populations anywhere from the thousands to the billions, they are statistically insignificant. After all, in most countries people are born every minute, so any calculation is going to be imprecise if only because it will change day to day.

Can the population REALLY continue to grow at that rate? In the Azores, for example, you would have a bit of trouble growing indefinitely, since they are rather small and only so many people actually would fit!

You are correct in pointing out that any growth rate is going to change over time. If I remember correctly, America's birthrate is actually negative, that is, below the replacement value of 2 per two people. That wasn't true 30 years ago.

70? Usually, it's 72.

You know, I had heard about a rule of 72 but couldn't remember what it was.

This is only a rough approximation and is a decent approximation only for a small range of values.

What is the range of values it works for? My populations range from thousands the a few billion. I could easily discard the small populations, but I need it to work for countries of millions and more.

The context is that this is a science fiction book, and there are ten "Guardians" each of whom has an area they study. For example, one person has the U.S. and Canada, another West Europe, another all island countries smaller than Iceland plus Native Peoples anywhere (in America Indians and Eskimos, in New Zealand Maori).

In the book, they have made public the existence of a Federation of Peoples made up of different races in this Galaxy (race as in Human Race, not Caucasian Race) Now they are trying to evaluate whether the people in each of the ten's areas is in favor of joining a Federation of Peoples or not.

The "final" draft of the book had been finished when I realized that I was using population numbers from 2009, 2010, and 2011 depending on the country, while the novel occurs in the Spring of 2017. Therefore all the population figures are incorrect. As a former journalist and in a few weeks a public speaker on "Researching For Writers," I figure I should get my numbers as accurate as is reasonably possible.

Thank you in advance for your second response. I don't mind logarithms and exponents, as the spreadsheet can figure them out easily. I was afraid it required calculus, which I never took (it wasn't offered in high schools in the late 1960s).

Ed Isenberg

 

[tkhunny]

The small range of values is the growth rate. The size of the population does not matter.

2% Real Doubling 35 years Rule of 72 36 years
4% Real Doubling 17.67 years Rule of 72 18 years
8% Real Doubling 9 years Rule of 72 9 years
16% Real Doubling 4.67 years Rule of 4.5 years

That's actually better at a wider range than I remembered.

The real calculation is this, if i = annual growth rate and n = number of years to double, n = log(2)/log(1+i). The base of the logartithm does not matter.
4% n = log(2)/log(1.04) = 17.672987685129713171989648133629

Some segments of the U.S. population are well over replacement. I think I read recently that Central American immigrants were doing well. Europeans were generally well below replacement. Middle Eastern countries generally well above. Of course there are pockets contrary to this.