Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 7 - Exponents and Exponential Functions - 7-6 Exponential Functions - Practice and Problem-Solving Exercises - Page 457: 39

Answer

The values are $\{1111.1,333.3,100,30,9,2.7\}$. Range is decreasing.

Work Step by Step

The given function is $y=100\cdot 0.3^x$ Substitute the values $x=\{-2,-1,0,1,2,3\}$ For $x=-2$. $\Rightarrow y=100\cdot 0.3^{(-2)}$ $\Rightarrow y=\frac{100}{0.3^2}$ $\Rightarrow y=\frac{100}{0.09}$ $\Rightarrow y=1111.1$ For $x=-1$. $\Rightarrow y=100\cdot 0.3^{(-1)}$ $\Rightarrow y=\frac{100}{0.3^1}$ $\Rightarrow y=\frac{100}{0.3}$ $\Rightarrow y=333.3$ For $x=0$. $\Rightarrow y=100\cdot 0.3^{(0)}$ $\Rightarrow y=100\cdot 1$ $\Rightarrow y=100$ For $x=1$. $\Rightarrow y=100\cdot 0.3^{(1)}$ $\Rightarrow y=100\cdot 0.3$ $\Rightarrow y=30$ For $x=2$. $\Rightarrow y=100\cdot 0.3^{(2)}$ $\Rightarrow y=100\cdot 0.09$ $\Rightarrow y=9$ For $x=3$. $\Rightarrow y=100\cdot 0.3^{(3)}$ $\Rightarrow y=100\cdot 0.027$ $\Rightarrow y=2.7$
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