Final answer:
The equation illustrating the per capita contribution to population growth in the exponential model is dN/dt = rN. It uses the intrinsic rate of increase (r), which is the difference between per capita birth and death rates. The logistic growth model further refines this with carrying capacity to model limited resource scenarios.
Step-by-step explanation:
The equation that illustrates the dependence of the per capita contribution to population growth on per capita birth and death rates in the exponential model for population growth is c) dN/dt = rN. This equation uses the terms birth rate (b) and death rate (d), and defines the intrinsic rate of increase (r) as r = b - d, which represents the per capita increase in population. It exemplifies the exponential model of growth, where the change in population size over an instant of time is directly proportional to the current population size (N). As such, this model assumes infinite natural resources, no immigration or emigration, and that rates of birth and death are constant over time.
However, in real-world scenarios, resources are limited, and to account for this, the logistic growth model is used which is represented by equation d) dN/dt = rN((K - N) / K). In this equation, K represents the carrying capacity of the environment and the term ((K - N) / K) is the fraction of the carrying capacity available for further growth. The logistic model describes how population growth slows as the population size approaches the carrying capacity.