Final answer:
The fastest population growth occurs when the birth rate exceeds the death rate and when immigration surpasses emigration. This positive growth rate is further supported by the presence of unlimited resources, though rapid growth can lead to negative consequences if not managed correctly.
Step-by-step explanation:
The condition that would lead to the fastest population growth is having a birth rate that is greater than the death rate, combined with immigration being greater than emigration. This scenario would result in the population increasing because more individuals are added through births and immigration than are lost through deaths and emigration. The population growth rate equation reflects this by having a larger positive value for the sum of the birth rate and immigration rate compared to the sum of the death rate and emigration rate.
When a population has unlimited resources like food, moisture, and oxygen, it can exhibit exponential growth. Yet, this rapid growth can have negative impacts if the environment cannot sustain the increased numbers, potentially leading to issues such as internal strife or forced emigration due to overpopulation and resource scarcity.