Final answer:
The rate of change of the bacteria population is directly proportional to the amount left. This relationship is indicative of exponential growth where population growth rate increases with population size.
Step-by-step explanation:
The relationship between the rate of change of the bacteria population and the amount left is best described as the first option which states that the rate of change of the bacteria population is directly proportional to the amount left. This directly proportional relationship indicates that as the population of bacteria, P, increases, the rate at which the population grows — its rate of change — also increases. This concept is often illustrated with exponential growth, where the growth rate, expressed by the variable r, accelerates as the population size escalates.
Exponential growth can be modelled by the equation dP/dt = rP, where dP/dt is the rate of change of the population, r represents the growth rate, and P denotes the population size. If resources were not limited, this would result in a J-shaped growth curve over time. However, real-world growth is often checked by factors such as resource limitations, competition, and predation, which may affect the rate of growth expressed in such models.