The population approaches the value of `M`.
As `k` is increased, the approach to steady state occurs more quickly. As `k` is decreased, the approach to the steady-state occurs more slowly.
As `P_0` increases, the solution starts farther along the original logistic curve.
If `P_0` is greater than `M`, the solution decreases to the steady-state value of `M`.
If `P_0=M`, the solution to the initial value problem is the constant function `P=M`.