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Gompertz & Logistic Explorer

Compare exponential, logistic, Gompertz, and linear growth models. Relevant to tumor dynamics, population growth, product adoption, and ecological modeling.

Parameters

50
0.15
2,000

Show Models

Model Insights

Logistic at day 30: 1395 / 2,000

Gompertz inflection: Day —

Gompertz reaches 50% K faster than Logistic — a key empirical finding in tumor biology.

Growth Curves (50 time units)

Day 0Day 5Day 10Day 15Day 20Day 25Day 30Day 35Day 40Day 45Day 500250005000075000100000
  • Exponential
  • Logistic
  • Gompertz

Phase Portrait — Logistic dV/dt vs. V

The logistic model predicts maximum growth rate at V = K/2 = 1,000

33100200300400500600700800900100011001200130014001500160017001800190020002100V-250255075

Model Equations

Exponential:

V(t) = V₀ · e^(r·t)

Logistic:

V(t) = K / (1 + ((K-V₀)/V₀)·e^(-r·t))

Gompertz:

V(t) = K · (V₀/K)^(e^(-r·t))

Linear:

V(t) = V₀ · (1 + r·t)