Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 5 - 5.4 - Exponential and Logarithmic Equations - 5.4 Exercises - Page 396: 65

Answer

$y=8e^{-\frac{2x}{3}}$ (Green) $y=11$ (Red) By observation of the graph: Solution: $x\approx-0.500$. It is just a visual approximation. Algebraically: $x=-0.478$
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Work Step by Step

$8e^{-\frac{2x}{3}}=11$ $e^{-\frac{2x}{3}}=\frac{11}{8}$ $\ln e^{-\frac{2x}{3}}=\ln\frac{11}{8}$ $-\frac{2}{3}x=\ln\frac{11}{8}$ $x=\frac{\ln\frac{11}{8}}{-\frac{2}{3}}=-0.478$
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