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 - Page 53: 7


Red: $10^{x}$ Green: $5^{x}$ Purple: $e^{x}$ Blue:$2^{x}$

Work Step by Step

These graphs are related initially because they are all exponential functions. In the modeled $y=b^{x}$ functions, as x increases the value of y will increase exponentially if $b>1$. Additionally, larger bases ($b$), increase at a faster rate. Hence, $10^{x} \gt 5^{x} \gt e^{x} \gt 2^{x}$ when we look at how fast the function increases. All of the graphs pass through the point (0,1) because any (nonzero) base to the 0th power is equal to 1.
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