Bounded growth for the rainbowfish

In the first module, we tried to predict the size of a rainbowfish population in an aquarium. Unfortunately, the growth of the population in the model of Section 1.4 was unbounded, and that of the improved model in Section 1.6 as well.

In this section, we will incorporate the limited capacity of the aquarium. When an aquarium gets crowded, the fish will lay fewer eggs, fewer young fish will survive and the fish may die earlier, so the growth of the population slows down. The problem statement is now:

An aquarium owner is breeding a population of rainbowfish. He starts with 30 rainbowfish and expects to sell 20 rainbowfish every day. The aquarium is large enough for a healthy population of 750. Predict the development of the size of the population.

In the next pages, bounded growth will be incorporated into the model, you will investigate the long-term solutions and validate them.