Growth Model Comparator
Logistic vs Exponential Growth
Formulas
Logistic Growth
\[ P(t) = \frac{K}{1 + Ae^{-rt}} \]
- \( K \): Carrying capacity
- \( A \): Determines initial condition
- \( r \): Growth rate
Exponential Growth
\[ P(t) = P_0 e^{rt} \]
- \( P_0 \): Initial population
- \( r \): Growth rate
Model Parameters
Results
Growth Visualization
About These Models
The logistic growth model describes how populations grow when constrained by limited resources.
Key characteristics:
- S-shaped (sigmoid) curve
- Growth slows as population approaches carrying capacity (K)
- Real-world examples: bacterial growth, animal populations in confined spaces
The exponential growth model describes unlimited growth where the rate is proportional to current size.
Key characteristics:
- J-shaped curve
- Constant growth rate leads to rapid increase
- Real-world examples: early-stage bacterial growth, compound interest
Comparison of the two models:
- Both models show similar growth patterns initially
- Exponential growth continues indefinitely
- Logistic growth slows and stabilizes at carrying capacity
- Exponential is unrealistic long-term for biological populations