Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.3 One-to-One Functions; Inverse Functions - 5.3 Assess Your Understanding - Page 282: 93



Work Step by Step

The general formula for an exponential function: $Ca^x+b=y$. The horizontal asymptote is $b$. With $b=2$, then the tentative equation is $Ca^x+2=y$. We plug in $x$ and $y$ values of each of the $2$ known points $(0,3)$ and $(1,5)$ to find the values of $C$ and $a$. For $(0, 3)$: $Ca^0+2=3\\ C+2=3\\ C=3-2\\ C=1. $ Thus, $y=1\cdot a^x+2 \longrightarrow y=a^x+2$. Use $(1, 5)$: $y=a^x+2\\ 5=a^1+2\\ 5=a+2\\ 5-2=a\\ 3=a$ Therefore, the equation is $y=3^x+2$.
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