The four-parameter Gompertz model is given by the expression
$$f(x) = c + (d-c)\exp(-\exp(b(\log(x)-e))).$$
The function is asymmetric about the inflection point, that is the parameter $\exp(e)$.
References
Seber, G. A. F. and Wild, C. J (1989) Nonlinear Regression, New York: Wiley & Sons (pp. 330--331).
See Also
Setting $c=0$ yields g3. A more flexible function, allowing fixing or constraining parameters, is gompertz.