Final answer:
The best function that represents an exponential population growth is 'f(x) = 14,000(0.05)^x' among the given options, as it is the only one that accounts for a percentage increase in population size each year.
Step-by-step explanation:
The student's question revolves around identifying which of the four given functions best represents a particular situation related to population growth of cities over time. To select the appropriate function, we need to consider the characteristics of exponential growth and linear increase.
Option Analysis
- f(x) = 14,000(0.05x) suggests a linear relationship, increasing the population by a constant amount each year.
- f(x) = 14,000(0.05) represents a static scenario where the population does not change over time.
- f(x) = 14,000(x + 0.05) also indicates a linear increase but with an initial small increment.
- f(x) = 14,000(0.05)x is the only option that represents an exponential growth model, where the population increases by a percentage each year.
If we are looking for a situation where the population of a city is expected to grow exponentially over the years, Option 4 is the best representation.