Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 4 - Exponential and Logarithmic Functions - Section 4.3 Exponential Functions - 4.3 Assess Your Understanding - Page 307: 89



Work Step by Step

The general formula for an exponential function can be defined as: $y=Ca^x+b~~~(1)$ Where we have the horizontal asymptote $=b$. So, in our case, we have: $y=Ca^x+2~~~(2)$ Plug in $x=0$ and $y=3$ to compute the values of $C$ and $a$. $Ca^0+2=3\\ C+2=3\\C=1 $ Thus, the equation (2) becomes: $y=a^x+2$ Now, plug in $x=1$ and $y=5$ to compute the values of $C$ and $a$. $y=a^x+2\\ 5=a+2\\ 5-2=a\\ a=3$ Thus, the required equation is $y=3^x+2$
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