Final answer:
The correct exponential model of population growth is represented by the equation N(t) = N(0)ert, and it's also expressed as dN / dt = rN when considering the rate of change over time.
Step-by-step explanation:
The question is asking which equation represents the exponential model of population growth. The correct option that reflects an exponential growth model of population is N(t) = N(0)ert. Here, N(t) is the population size at time t, N(0) is the initial population size, r is the intrinsic rate of increase, and e is the base of the natural logarithm. This model assumes unlimited resources and no restrictions on population growth, which is why the population grows exponentially.
Another form of this equation presented as a differential equation is dN / dt = rN, where dN/dt represents the rate of change in population size over an infinitesimally small interval of time. Essentially, it states that the rate of population change (growth) at any time is directly proportional to the population size at that time. This differential equation can be solved to yield the exponential equation N(t). It's important to note that in real-world scenarios, resources are rarely unlimited, leading to a more realistic logistic growth model which accounts for limited resources.