Final answer:
To represent exponential growth, a table must show values that multiply consistently at each interval, such as doubling in a sequence. Logistic growth, represented by an S-curve, increases exponentially initially but levels off due to resource limits. Exponential growth tables follow the pattern of increasing by a factor of 2^n after 'n' doubling times.
Step-by-step explanation:
The question 'Which table represents exponential growth?' pertains to the mathematical concept of growth patterns. Exponential growth is defined by each successive value being a multiple of the previous value, with the rate of growth being constant in percentage terms. A sequence such as 2, 4, 8, 16 exemplifies exponential growth because each value is double the preceding one, representing a constant doubling time. For a table to represent exponential growth, it would need to demonstrate this pattern of multiplicatively increasing values.
In contrast, logistic growth, often represented by an S-curve, shows an initial exponential increase until it begins to level off as it approaches its carrying capacity. Logistic growth typically occurs in populations where resources become limited as the population size approaches the carrying capacity of the environment.
An investigation of tables representing growth should seek a sequence where, after 'n' doubling times, the increase is a factor of 2^n, where 2 is the base and 'n' is the number of doubling times. The exponential model is often used as a simplified representation of growth, which in reality may be better described by more sophisticated models incorporating factors such as resource limitations, as in the logistic growth model.