1. What is the Population Growth Formula?

The exponential population growth formula models how a population changes over time when growth is unrestricted. It's commonly used in biology, ecology, and demographics to predict population sizes under ideal conditions.

2. How Does the Calculator Work?

The calculator uses the exponential growth equation:

Where:

• \( P_t \) — Final population size
• \( P_0 \) — Initial population size
• \( r \) — Growth rate (per year)
• \( t \) — Time period (years)
• \( e \) — Euler's number (~2.71828)

Explanation: The formula assumes continuous growth at a constant rate. The population increases exponentially when r > 0 and decreases when r < 0.

3. Applications of Population Growth

Details: This model is used for predicting bacterial growth, wildlife populations, human demographics, and compound interest in finance. It works best for populations with unlimited resources.

4. Using the Calculator

Tips: Enter initial population (must be positive), growth rate (can be positive or negative), and time period (must be non-negative). Growth rate of 0.02 represents 2% growth per year.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between exponential and logistic growth?
A: Exponential assumes unlimited resources while logistic accounts for carrying capacity of the environment.

Q2: How do I convert percentage growth to the rate (r)?
A: Divide percentage by 100. For example, 5% growth becomes r = 0.05.

Q3: What does negative growth rate mean?
A: A negative rate indicates population decline over time.

Q4: When is this model not appropriate?
A: When resources are limited, or for populations with complex age structures or migration.

Q5: How can I calculate doubling time?
A: Doubling time ≈ 70 divided by the growth rate percentage (e.g., 7% growth → ~10 years to double).