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 Test - Page 491: 2

Answer

$\text{exponential decay}$; $y$-intercept = $2$

Work Step by Step

RECALL: The exponential function $y=c \cdot a^x$ represents an exponential: (i) decay when $0\lt a \lt 1$; (ii) growth when $a \gt 1$ The given function can be written as: \begin{align*} y&=2\left(6\right)^{-1(x)}\\ y&=2\left(6^{-1}\right)^x\\ y&=2\left(\frac{1}{6}\right)^x \end{align*} Thus, the given exponential function has $a=\frac{1}{6}$ which is less than $1$. Thus, the given function represents exponential decay. The $y$-intercept of a function can be found by sestting $x=0$ then solving for $y$. Hence, the $y$-intercept is \begin{align*} y&=2 \cdot \left(6\right)^{-x}\\ y&=2 \cdot 6^0\\ y&=2 \cdot 1\\ y&=2 \end{align*}
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