dtdP==f(P)rPln(M/P), the Gompertz Equation - Sketch the graph of f(P) versus P, find the critical points, and determine if each is asymptotically stable or unstable. - For 0P(t)M, determine where the graph of P(t) versus t is concave up and where it is concave down. - For each P satisfying 0P(t)M, show that dP/dt, as given by (5) is never less than dP/dt as given by the logistic equation (use the version of the logistic equation in this question). - Use the substitution u=ln(P/K) to convert equation (5) into an ODE that you are familiar with. Using this technique, solve the ODE (5) subject to the initial condition P(0)=P0. dtdP==f(P)rPln(M/P), the Gompertz Equation - Sketch the graph of f(P) versus P, find the critical points, and determine if each is asymptotically stable or unstable. - For 0P(t)M, determine where the graph of P(t) versus t is concave up and where it is concave down. - For each P satisfying 0P(t)M, show that dP/dt, as given by (5) is never less than dP/dt as given by the logistic equation (use the version of the logistic equation in this question). - Use the substitution u=ln(P/K) to convert equation (5) into an ODE that you are familiar with. Using this technique, solve the ODE (5) subject to the initial condition P(0)=P0