Final answer:
The constant growth model refers to exponential growth (option b) in mathematics, depicted as a J-shaped curve, where the growth rate increases as the population size grows, eventually leading to logistic growth when resources become limited.
Step-by-step explanation:
The constant growth model in mathematics that is being referred to in the context of population growth is represented by exponential growth. This occurs when the growth rate of a value, such as a population, is proportional to its current size, leading to a growth pattern where the increase accelerates over time. The number of individuals in a population, for instance, might double every month, which is a classic example of exponential growth. This is depicted as a J-shaped curve and the growth rate becomes faster as the population size increases.
However, this model is an idealization and in real situations, eventually resources will become limited and the logistic growth model takes over. In logistic growth, the population increase slows down as resources become scarcer, eventually levelling off when the carrying capacity of the environment is reached, resulting in an S-shaped curve.