Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 7 - Exponential and Logarithmic Functions - Chapter Review - Page 488: 12


$\text{exponential decay;}$ $y$-intercept = $2.25$

Work Step by Step

Recall: The exponential function $y=c \cdot b^x$ involves: (1) an exponential growth if $b\gt1$. (2) an exponential decay if $0\lt b \lt1$. The given exponential function has $b=\frac{1}{3}$, which is less than $1$. Thus, the function is an example of exponential decay. The $y$-intercept of an exponential function can be found by setting $x=0$ then solving for $y$. Hence, the $y$-intercept of the given function is: \begin{align*} y&=2.25\left(\frac{1}{3}\right)^0\\ y&=2.25 \cdot 1\\ y&=2.25 \end{align*}
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