Another equation that has been used to model population growth is the Gompertz14 equation dy/dt=ryln(K/y), where r and K are positive constants.
a) Sketch the graph of f(y) versus y, find the critical points, and determine whether each is asymptotically stable or unstable.
b) For 0≤y≤K, determine where the graph of y versus t is concave up and where it is concave down.
c) For each y in 0<y≤K, show that dy/dt as given by the Gompertz equation is neverless than dy/dt as given by the logistic equation.