Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 4 - Exponential Functions - 4.5 The Number e - Exercises and Problems for Section 4.5 - Exercises and Problems - Page 175: 44

Answer

$a=b>1$, $k>0$, $l<0$

Work Step by Step

Since the graphs of $a e^{k x}$ and $b e^{l x}$ have the same vertical intercept, we know $a=b$. Also $a=b>1$ because the vertical intercepts of $a e^{k x}$ and $b e^{l x}$ is above $e^{ x}$. Since $ae^{k x}$ increases as $x$ increases, we know $k>0$. Because $be^{lx}$ decreases and $b>0$, it means $l<0$.
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