In AP Environmental Science (APES), understanding population dynamics is a core competency. Whether you are analyzing human demographics or animal populations in an ecosystem, calculating the growth rate allows you to predict future population sizes and resource requirements. This guide covers the essential formulas and concepts you need to master for the APES exam.
The Core Population Formula
Population growth is determined by four main factors: Births, Deaths, Immigration (individuals entering a population), and Emigration (individuals leaving a population). The relationship between these factors defines whether a population is growing, shrinking, or stabilizing.
Population Change = (Births + Immigration) – (Deaths + Emigration)
In shorthand variables often used in textbooks:
B = Births
D = Deaths
I = Immigration
E = Emigration
Calculating the Growth Rate (r)
The growth rate, denoted as r, is typically expressed as a percentage. It represents the rate at which individuals are added to the population per initial individual, multiplied by 100.
It is important to distinguish between global and local populations:
Global Population Growth: Since people do not leave the planet (yet), Immigration and Emigration are zero. The formula simplifies to: (CBR - CDR) / 10.
Local/National Population Growth: Includes Immigration and Emigration.
Crude Birth and Death Rates (CBR & CDR)
On the APES exam, data is often given as Crude Birth Rate (CBR) and Crude Death Rate (CDR), which are measured per 1,000 individuals rather than as raw totals.
To convert these to a percentage growth rate, use this simple shortcut:
One of the most frequent calculations in APES is finding the Doubling Time—the number of years it takes for a population to double in size at a constant growth rate. This is found using the Rule of 70.
Doubling Time (years) = 70 / r (in percent)
Note: When using the Rule of 70, keep r as a percentage (e.g., use 2 for 2%), do not convert it to a decimal (0.02).
Example Calculation
Imagine a population of 10,000 deer. Over one year, there are 500 births, 300 deaths, 50 immigrants, and 20 emigrants.
Population demographics influence environmental impact (I = PAT formula), resource depletion, and biodiversity loss. High growth rates in developing nations typically correlate with the early stages of the Demographic Transition Model, while low or negative growth rates are characteristic of post-industrial societies.
function calculateGrowth() {
// Get input elements
var initialPopInput = document.getElementById('initialPop');
var birthsInput = document.getElementById('births');
var deathsInput = document.getElementById('deaths');
var immigrationInput = document.getElementById('immigration');
var emigrationInput = document.getElementById('emigration');
// Parse values, defaulting to 0 if empty
var N0 = parseFloat(initialPopInput.value);
var B = parseFloat(birthsInput.value) || 0;
var D = parseFloat(deathsInput.value) || 0;
var I = parseFloat(immigrationInput.value) || 0;
var E = parseFloat(emigrationInput.value) || 0;
// Validation
if (isNaN(N0) || N0 0) {
doublingTime = 70 / growthRate;
dtDisplay = doublingTime.toFixed(1) + " Years";
} else if (growthRate === 0) {
dtDisplay = "Infinite (Stable)";
} else {
dtDisplay = "N/A (Shrinking)";
}
// Display Results
var resultsDiv = document.getElementById('results');
resultsDiv.style.display = 'block';
document.getElementById('resNetChange').innerHTML = (netChange > 0 ? "+" : "") + netChange;
document.getElementById('resFinalPop').innerHTML = finalPop.toLocaleString();
document.getElementById('resGrowthRate').innerHTML = growthRate.toFixed(3) + "%";
document.getElementById('resDoublingTime').innerHTML = dtDisplay;
}