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 - 4.3 Graphs of Exponential Functions - Exercises and Problems for Section 4.3 - Exercises and Problems - Page 163: 35

Answer

a) All constants are positive. b) $b$ c) $b$, $a$, $c$, $p$ d) $a=c$ e) $d$ and $q$

Work Step by Step

(a) All constants are positive. (b) The constant $b$ is between 0 and 1 , because $y=a \cdot b^x$ represents a decreasing function. (c) In addition to $b$, the constants $a, c, p$ could be between 0 and 1 . (d) Since the curves $y=a \cdot b^x$ and $y=c \cdot d^x$ cross on the $y$-axis in the same point, we must have $a=c$. (e) The values of $a$ and $p$ are not equal because curves cross the $y$ axis at different points. The values of $b$ and $d$ and, as well as, $b$ and $q$ cannot be equal as one is between $0$ 1nd $1$, while the other is greater than $1$. However, $d$ and $q$ could be equal.
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