Answer
The function models the data well for the values attributed to the year 2,010.
Work Step by Step
$$f(x) = \frac{12.57}{1 + 4.11e^{-0.026x}}$$ where $f(x)$ is the world population in billions and $x$ represents the amount of years after 1949. To compare the world population in the year 2010: $$f(x) = \frac{12.57}{1 + 4.11e^{-0.026(2,010 - 1,949)}}$$ $$f(x) = \frac{12.57}{1 + 4.11e^{-0.026(61)}} \approx 6.8$$ We can conclude that, if the world population is to be 6.9 billion in the year 2,010, then the model is only off by 100 million, which is a good estimate.
