Remarks about the solutions to the exercises

The solutions to ex 1,2 are similar to the solutions to the examples discussed on p1, and their graphs (Figures 3,4) are all fairly similar (one equilibrium value, and if the initial population is less than that, then P grows to that value and levels off, whereas if the initial population is more than that, then P decreases to that value and levels off).

However, the solution to ex 3 is a bit different. In finding when P' is 0, you have to solve a quadratic equation in P, giving (generally) two solutions, two equilibrium values. Depending on the actual values of the various constants, the lower one could be quite close to 0, and barely shows on the graph (Figure 5), but if it's higher (or if your scale is big enough!), then it shows clearly, and you can see the general behaviour better (Figure 6). Which is: two equilibrium values, and if P starts lower than the lower one, P will (quickly) decrease to 0; if P starts between the lower one and the higher one, P will increase to the higher equilibrium value; and if P starts higher than the higher one, P will decrease to the higher equilibrium value (Figure 6).