Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 3 - Review Exercises - Page 513: 80


The number of miles is $5.5\text{ miles}$.

Work Step by Step

As per the question, $ P\left( x \right)=14.7{{e}^{-0.21x}}$ Substitute the values of $ P\left( x \right)$ in the above equation and simplify: $4.6=14.7{{e}^{-0.21x}}$ And divide both sides of the equation by $14.7$ and simplify as follows: $\begin{align} & \frac{4.6}{14.7}=\frac{14.7}{14.7}{{e}^{-0.21x}} \\ & 0.31={{e}^{-0.21x}} \end{align}$ Write the above exponential form in logarithmic form using: If ${{b}^{y}}=x $, then ${{\log }_{b}}x=y $ So, $0.31={{e}^{-0.21x}}$ is equivalent to ${{\log }_{e}}0.31=-0.21x $. Solving the above expression as follows: $\begin{align} & {{\log }_{e}}0.31=-0.21x \\ & -1.17=-0.21x \end{align}$ Change the sides of the equation and divide both sides by $-0.21$, $\begin{align} & \left( \frac{-0.21}{-0.21} \right)x=\frac{-1.17}{-0.21} \\ & x=5.5 \end{align}$ Thus, the peak of Mt. Everest is $5.5\text{ miles}$ above sea level.
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