Logistic model of population growth/decay

This Geogebra applet enables you to experiment with the behaviour of the solution of the logistic model.
Of special interest is the case when the initial population is positive but less than half the population carrying capacity N. In that case, the population grows more and more rapidly until it reaches a level of N/2. After that, it continues to grow but at a decreasing rate, approaching N as time tends to infinity.