Answer
The function models the data well when compared with actual values for the year 2,000.
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 2000: $$f(x) = \frac{12.57}{1 + 4.11e^{-0.026(2,000 - 1,949)}}$$ $$f(x) = \frac{12.57}{1 + 4.11e^{-0.026(51)}} \approx 6.01$$ We can conclude that, if the world population is to be 6.1 billion in the year 2,000, then the model is only off by 90 million, which is a good estimate.