Final answer:
In a logistic population growth, the change in population size over time is the greatest when the population is halfway to its carrying capacity. This is known as the log phase of growth.
Step-by-step explanation:
In a logistic population growth, the change in population size (dn) over the change in time (dt) is the greatest when the population is halfway to its carrying capacity. At this point, the population growth rate is at its maximum, resulting in the steepest slope on a graph of population size over time.
For example, in the logistic growth of a bacterial population, the growth rate is highest during the log phase when the population is rapidly increasing but has not yet reached its maximum capacity.