Final answer:
It is true that if the instantaneous per capita rate of growth (r) of a population is greater than zero, the population is growing. This rate accounts for births, deaths, immigration, and emigration, which combined determine whether the population size increases, decreases, or remains constant.
Step-by-step explanation:
The statement that the instantaneous per capita rate of growth (r) of a growing population is greater than zero is true. The value "r" represents the net change in population size over time, accounting for births, deaths, and migrations. When r is greater than zero, it indicates that the births plus immigration are exceeding deaths plus emigration, resulting in an overall increase in population size.
The birth rate (b) and the death rate (d) are critical components used to calculate r. This calculation is encapsulated in the formula r = (b + i) - (d + e), where i stands for immigration and e for emigration. This value can be positive, negative, or zero, signifying a growing, decreasing, or steady population, respectively. A positive r suggests that the population is experiencing growth. Various species have different intrinsic rates of increase, or biotic potential, depending on their capacity for reproduction under ideal conditions. Consequently, a species with an inherent high biotic potential, like bacteria, can grow much faster than a species with a lower biotic potential, like humans.