The population growth rate dP/dt = rP(1-P/k), where r and k are an positive constant. Suppose that the initial population is P_0. Discuss, by considering the sign of dP/dt, the relationship between P and k if P_0 is less than k and if P_0 is greater than k.

How to show their relationship? Can I consider P as P_0 ? And by what condition? Somebody please guide me and explain it to me. Please take your time and THANK YOU VERY MUCH~~!!!