🎓 Biology • Ecology
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Population Growth Calculator (Exponential & Logistic)
Models ecological population growth over time using exponential N(t) = N0·e^(rt) and density-dependent logistic carrying capacity (K) models.
⭐ Ecological Population Presets:
Population Growth Dynamics: Exponential vs. Logistic S-Curve
Compares unconstrained exponential expansion with resource-limited density-dependent carrying capacity ($K$)
per unit time
days / years
Environmental max
Exponential Model N(t) = N₀ · e^(rt)
448 indiv.
Doubling Time: 13.9 time units ($t_d = \frac{\ln 2}{r}$)
Logistic Model (Capped at K = 1,500)
364 indiv.
Inflection Point ($K/2$): 750 ind. at $t \approx 52.8$
Ecology Growth Simulation: Exponential J-Curve vs. Logistic S-CurveCarrying Capacity K = 1500
Logistic S-Curve: 364 Exponential J-Curve: 448 Carrying Capacity K: 1500
Population Growth Dynamics
Populations grow exponentially when resources are unlimited, but transition to a sigmoidal (S-shaped) logistic curve as carrying capacity (K) imposes environmental resistance.
Formula & Step-by-Step Calculation
Exponential: N(t) = N₀ · e^(rt), Logistic: dN/dt = rN(1 - N/K)
r = intrinsic growth rate, K = carrying capacity of the environment.
Worked Step-by-Step Examples
Example 1
Starting population 100 with r = 0.05 per year after 20 years
Solution: Exponential: 272 individuals; Logistic (K=1000): 253 individuals
• N(20) = 100 × e^(0.05 × 20) = 100 × e^1 ≈ 271.8
Common Real-World & Academic Use Cases
- ✓ Wildlife conservation herd projections
- ✓ Bacterial culture growth kinetics
- ✓ Fisheries sustainable harvest limits
How to Use the Population Growth Calculator (Exponential & Logistic)
1
Enter Initial Population N₀
Input initial count.
2
Set Growth Rate & Carrying Capacity
Input r and K.
3
Review Population Projections
Compare exponential vs logistic numbers.
Frequently Asked Questions
Q: What is carrying capacity K?
The maximum population size of a biological species that a specific environment can sustain indefinitely.