1. What is the Population Growth Equation?

The exponential population growth equation models how a population changes over time when growth is unrestricted. It's based on the principle that population growth rate is proportional to the current population size.

2. How Does the Calculator Work?

The calculator uses the exponential growth equation:

Where:

• \( P_t \) — Future population size
• \( P_0 \) — Initial population size
• \( r \) — Growth rate (expressed as a decimal)
• \( t \) — Time period
• \( e \) — Euler's number (~2.71828)

Explanation: The equation shows how population grows exponentially when resources are unlimited. The growth rate compounds continuously over time.

3. Importance of Population Growth Calculation

Details: Understanding population growth helps in urban planning, resource allocation, environmental impact assessment, and economic forecasting.

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 should be in decimal form (e.g., 0.03 for 3% growth).

5. Frequently Asked Questions (FAQ)

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

Q2: How do I convert percentage growth rate to decimal?
A: Divide the percentage by 100 (e.g., 2.5% becomes 0.025).

Q3: Can this model negative growth?
A: Yes, use a negative growth rate to model population decline.

Q4: What are limitations of this model?
A: It doesn't account for resource limits, density-dependent factors, or changes in growth rate over time.

Q5: How accurate is this for long-term predictions?
A: Less accurate for long periods as real populations face constraints not modeled in simple exponential growth.