Population Growth Calculator
Model how populations grow over time using exponential or logistic growth equations. Enter initial size, growth rate, and time to generate a complete population projection table.
Population Growth Models
N(t) = N₀ × e^(r × t)Two fundamental models describe population growth in ecology: Exponential growth assumes unlimited resources — the population increases by a constant percentage per unit time. Logistic growth adds a carrying capacity (K) that represents the maximum sustainable population size, creating the characteristic S-shaped curve as growth slows near K.
| Symbol | Variable | Description |
|---|---|---|
| N(t) | Population at time t | The size of the population after time t has passed. |
| N₀ | Initial population | Population size at time zero (the starting point). |
| r | Intrinsic growth rate | Rate of natural increase (births minus deaths per individual per time unit). Expressed as a decimal. |
| t | Time elapsed | How much time has passed since the initial population count. |
| K | Carrying capacity | (Logistic only) Maximum population the environment can sustainably support. |
| e | Euler's number | Mathematical constant ≈ 2.71828, base of natural logarithm. |
How to Use This Calculator
- 1
Choose your model
Use Exponential Growth for populations with unlimited resources (bacteria in early culture, invasive species). Use Logistic Growth for real populations that face resource limits.
- 2
Enter parameters
Provide initial population (N₀), intrinsic growth rate (r as a decimal), and time period. For logistic model, also enter the carrying capacity (K).
- 3
View results and table
The calculator shows the final population size and a step-by-step projection table showing population at each time increment.
- 4
Interpret the table
For logistic growth, watch for the inflection point — the growth rate is maximum when the population reaches K/2. After that, growth decelerates until K is approached asymptotically.
Frequently Asked Questions
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