How long would it take a population to double? That's an important question, and in this lesson, we are going to explore one of the easy ways that statisticians can calculate that number.
There are a lot of people in this world, and that number just keeps increasing. Wouldn't it be nice if we had a simple formula to help us predict just how large our population could actually get? Well, we do. Doubling time is the amount of time it takes for a value to double itself at a consistent rate of growth. It can be applied to any value that increases at a consistent rate, but we very often use it to study human population growth.
Around the world, people in similar situations tend to reproduce at similar rates, and so the rates of growth throughout human history have been surprisingly consistent. So, ideas like doubling time are very useful to help us prepare for the future. What sort of infrastructure will we need? How much space will a population need? What amount of resources will they use? These questions all require an understanding of future population sizes. So, this is an important field of study. Let's get to it, on the double.
The Rule of 70
To figure out how long it would take a population to double at a single rate of growth, we can use a simple formula known as the Rule of 70. Basically, you can find the doubling time (in years) by dividing 70 by the annual growth rate.
Imagine that we have a population growing at a rate of 4% per year, which is a pretty high rate of growth. By the Rule of 70, we know that the doubling time (dt) is equal to 70 divided by the growth rate (r). That means our formula would look like this:
dt = 70 / r
dt = 70 / 4
dt = 17.5
At their present rates of growth, what is the doubling time for each of these nations?
Use and Implications
So, now we know that at an annual growth rate of 4%, a population will double in 17.5 years. It's very important to note that when plugging in the formula, you enter the growth rate as a whole number, not as a decimal. Even though 4% is usually seen in equations as .04, for example, in this case you just enter it as 4.
This same formula can be used in reverse. Say you want to know what rate of population growth would have to be sustained in order to double your population in 10 years. In this case, we know the doubling time (10 years), but not the annual growth rate. So, let's plug that back into the formula.
10 = 70 / r
10r = 70
r = 70 / 10
r = 7
So, if you want to double your population in 10 years, you have to maintain an annual growth rate of 7%.
Over 83,000 lessons in all major subjects
Get access risk-free for 30 days,
just create an account.
The Rule of 70 is a useful tool, but there are some things we have to remember about it. This formula only works if the annual growth rate remains completely consistent. That means we are dealing with issues of exponential growth, in which a value increases by a constant rate. In the real world, we can't actually expect human populations to grow at the exact same rate, year after year. In fact, there comes a point when every population reaches its natural limit of what can be sustained in that environment. We call this the carrying capacity. At this point, population growth tends to level off.
Even if it is not perfectly unwavering, the human population has increased at a fairly consistent rate of exponential growth
As a result, doubling time is used more as a way to estimate future population averages. We don't expect these numbers to be 100% accurate, but we do expect that they'll represent a relatively close estimate. Still, it can be a very useful tool. In some places with lower populations, increasing the population is seen as beneficial. You create a larger society with more economic power. In other cases, policymakers need to know how to prepare for the future. Can they sustain this rate of growth? How long do they have to prepare for a doubled population? These are important questions, and luckily there's a simple formula to help.
Let's take a moment to review what we've learned.
The doubling time is the amount of time it would take a value to double at a consistent rate. It is a way to measure exponential growth, and does require the assumption that the growth rate will not change, since exponential growth is when a value increases by a constant rate. This number can be found using the Rule of 70, which describes the formula dt = 70 / r, where dt is the doubling time, and r is the annual rate of growth. This is just a way to estimate the future population and doesn't take into account changes in growth rate or carrying capacity, which is a point when every population reaches its natural limit of what can be sustained in that environment, but it can still be a very useful tool that helps us prepare for a rapidly changing world.
In the following problems, students will calculate the doubling time for different populations using the rule of 70. The annual rate of growth will also be solved for given the doubling time of the population.
1. A population of rabbits grows at an annual growth rate of 14%. What is the doubling time of the rabbit population? How long will it take for the rabbit population to quadruple?
2. If a population of people has a doubling time of 19 years, what is the annual growth rate of the population? Round to 3 decimal places.
3. Your friend calculated the doubling time for a population with annual growth rate of 5% as follows: dt = 70 / 0.05 = 1,400 years. What is wrong with this calculation? What is the correct doubling time?
1. To calculate the doubling time using the rule of 70, we have dt = 70 / 14 = 5. So the doubling time of the rabbit population is 5 years. This means that the population doubles every 5 years and so the population will quadruple (double twice) in 5*2 = 10 years.
2. Using the formula dt = 70 / r we can solve for the annual growth rate. We have 19 = 70 / r and so 19r = 70. Dividing by 19 gives r = 70 / 19 which is about 3.684%.
3. Your friend mistakenly converted the percentage to its decimal form, 0.05, rather than using 5 in the calculation. The correct doubling time is dt = 70 / 5 = 14 years.
Register to view this lesson
Are you a student or a teacher?
Unlock Your Education
See for yourself why 30 million people use Study.com
Did you know… We have over 220 college
courses that prepare you to earn
credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the
first two years of college and save thousands off your degree. Anyone can earn
credit-by-exam regardless of age or education level.