College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.5 - Page 506: 40

Answer

The world population will reach 7 billion by the year 2,012.

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: $$f(x) = 7 = \frac{12.57}{1 + 4.11e^{-0.026(x)}}$$ $$7(1 + 4.11e^{-0.026x}) = 12.57$$ $$7 + 28.77e^{-0.026x} = 12.57$$ $$28.77e^{-0.026x} = 5.57$$ $$e^{-0.026x} = \frac{5.57}{28.77}$$ $$-0.026x = \ln (\frac{5.57}{28.77})$$ $$x = -\frac{\ln (\frac{5.57}{28.77})}{0.026} \approx 63$$We can conclude that, when the world population reaches 7 billion, the year will be approximately 1,949 + $63$ = 2,012.
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