Answer
The world population will reach 8 billion by the year 2,025.
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 find when the world population will reach 7 billion: $$f(x) = 8 = \frac{12.57}{1 + 4.11e^{-0.026(x)}}$$ $$8(1 + 4.11e^{-0.026x}) = 12.57$$ $$8 + 32.88e^{-0.026x} = 12.57$$ $$32.88e^{-0.026x} = 4.57$$ $$e^{-0.026x} = \frac{4.57}{32.88}$$ $$-0.026x = \ln (\frac{4.57}{32.88})$$ $$x = -\frac{\ln (\frac{4.57}{32.88})}{0.026} \approx 76$$We can conclude that, when the world population reaches 8 billion, the year will be approximately 1,949 + $76$ = 2,025.
