Could the following statements about theoretical growth curves for predators and prey actually represent what happens in nature?1. The prey...

I think, in general, you can make a case that this course of events is typical in nature.  The problem is that it is very simplified.  There are a lot of other factors that exist that might mess up such a curve.

1. The prey population rises. This, in itself, requires a lot of conditions.  Lets assume that it is a bounty year, the prey animal has lots of food, and no other factors affect the population.  Then a population would likely increase.

2. Predator population rises due to increase in prey population. This probably would occur.  Whatever it is that eats the prey animal would have more food, resulting in more babies reaching maturity.  One stumbling block here might have to do with certain herd populations.  Some prey animals are better protected within a strong herd that offers mutual defense. This would actually make predator populations remain steady or sink.

3. Prey population falls due to increase in predation. Maybe.  This depends on the rate or reproduction for the prey population.  If the prey population breeds faster and in greater numbers than the predator population the prey numbers will continue to grow despite the increase in predators.

4. Predator population falls due to decline in prey population. This assumes that the two breed at a similar rate, but yes, if the prey population were to fall in response to predation than after a while the lack of food would result in fewer predators being able to survive.  But remember, food is only one of the components of an effective ecosystem.

5. Prey population rises due to decline in predator population. Again, maybe.  Predator populations are only one factor when it comes to the proliferation of prey.  Food sources and diseases can plague a large population of prey.  It is possible that the prey population would not rise with the decline in predators as a result of one of these factors.

So, in short, I think you can make a generalization that prey and predator populations are related in such a way.  It's just that in nature things aren't always so black and white.

Hope this helps!