Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.4 - Exponential Functions - 1.4 Exercises: 8

Answer

For $x\gt 0$, $8^x\gt e^x$ and $8^{-x}\lt e^{-x}$. All of the functions pass through the point $(0,1)$.
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Work Step by Step

The graphs are on the figure below. All of them pass through the point $(0,1)$. If exponential is $x$ then for $x>0$ the bigger the base the bigger the value of the function for $x<0$ the bigger the base the smaller the value of the function. If exponential is $-x$ then for $x>0$ the bigger the base the smaller the value of the function for $x<0$ the bigger the base the bigger the value of the function. Since $8>e$, then: for $x\gt 0$, $8^x\gt e^x$ and $8^{-x}\lt e^{-x}$.
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