Gompertz Equation

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dx_t/dt=rx_tlog(K/x_t) ⇔ x_t=K exp{log(x₀/K)e^-rt}

This model is similar to the logistic growth model. In this model, density effect is integrated as the term of log(K/x_t). The population value converges to carrying capacity, K value.

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dxt/dt=rxtlog(K/xt) ⇔ xt=K exp{log(x0/K)e-rt}

dx_t/dt=rx_tlog(K/x_t) ⇔ x_t=K exp{log(x₀/K)e^-rt}