A mathematical model for tumor growth is given by dX/DT =c ln (k/x) where X = X(t) is the size of the tumor, is

A mathematical model for tumor growth is given by dX/DT =c ln (k/x)  where X = X(t) is the size of the tumor, κ is the carrying capacity, i.e. the maximum size that can be reached with the available nutrients, lim t→∞ X(t) = κ, and c is a constant related to the proliferative ability of the cells. The solution to this differential equation is known as the Gompertz curve or Gompertz function. Derive this solution. Check that your solution satisfies Lim t→∞ X(t) = κ.