Final answer:
Biology, pertaining to population dynamics, is the subject matter, with a focus on exponential and logistic growth models for explaining ant colony expansion. The correct answer is option a.
Step-by-step explanation:
The subject of this question is Biology, specifically the concepts of population dynamics and population growth models. The question is most suitable for the High School grade level, involving the study of how biological populations expand and contract over time.
When a newly mated queen ant founds a nest, the initial population growth is typically exponential because the population size is small and resources are plentiful. The growth rate in this phase doubles over regular intervals, which means that the population grows by a constant proportion rather than a constant amount. However, as the colony grows, resources such as food and space will start to become scarce, leading to competition among the ants. This results in a transition to a logistic growth model, where the growth rate decreases as the population size approaches the carrying capacity of the environment, eventually leveling off.
An example of exponential growth is bacteria growing in an enriched medium in a lab. The population of bacteria will double in a constant time period, leading to a rapid increase in numbers. On the other hand, logistic growth is illustrated by a population that initially grows exponentially but then slows down as factors like food shortage or waste accumulation start to limit further growth. Eventually, the growth rate levels off to zero, typically creating an S-shaped curve on a graph.
Therefore, the equation likely to best describe the population growth of the new ant colony would be logistic (option A).