Population Growth Calculator

Historical Background

Population growth has been a subject of interest for demographers and scientists for centuries. Historically, Thomas Malthus, in his "Essay on the Principle of Population" (1798), discussed exponential population growth and its consequences, linking it to the availability of resources. This concern remains pertinent, especially as the global population continues to rise.

Calculation Formula

To calculate the future population after a given period of time, we use the following formula:

\[ x(t) = x_0 \times (1 + r)^t \]

where:

• \(x(t)\): Final population after time \(t\).
• \(x_0\): Initial population.
• \(r\): Growth rate (in decimal form).
• \(t\): Number of years (or time period).

Example Calculation

Let's apply the formula to two examples:

Example 1:

• Initial population (\(x_0\)): 10,000
• Growth rate (\(r\)): 12% per year (0.12)
• Time period (\(t\)): 5 years

\[ x(t) = 10,000 \times (1 + 0.12)^5 = 17,958.56 \]

Example 2:

• Initial population (\(x_0\)): 10,000
• Growth rate (\(r\)): 15% per month (0.15)
• Time period (\(t\)): 20 months

\[ x(t) = 10,000 \times (1 + 0.15)^{20} = 163,666 \]

Common FAQs

What is population growth?
Population growth is the increase in the number of individuals in a population due to reproduction and immigration.

What is a population growth rate?
The population growth rate refers to the rate at which a population increases annually or within another specified period.

What type of growth do populations typically see?
Populations usually experience exponential growth, but eventually, limiting factors such as resource availability lead to a slowdown.