Consider again the logistic differential equation from the previous question, dn dt

= kn 

1 −

n K



.

Without solving the equation (i.e., using a qualitative analysis)

In other words, if the population can grow, it will, until the maximal population is reached. However, if the populations starts out too large, it will decrease until it reaches the maximal sustainable level.

show that any solution with 0 < n(0) < K will increase until n ≈ K. Show also that any solution with n(0) > K will decrease until n ≈ K.