Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 9 - Section 9.2 - Exponential Functions and Models - Exercises - Page 642: 6

Answer

$\begin{array}{|c|r|r|r|r|r|r|r|} \hline x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline g(x) &2/27 & 2/9 & 2/3 & 2 & 6 & 18 & 54 \\ \hline \end{array}$ Technology formula:$\quad $2*(3^x)$ \quad$ or$ \quad $2*3^x

Work Step by Step

Technology formula:$\quad $2*(3^x)$ \quad$ or$ \quad $2*3^x. PEMDAS (acronym for order of operations) has exponents before multiplication, so the parentheses are not necessary, although they are not an error. $f(-3)=2(3^{-3})=\displaystyle \frac{2}{3^{3}}=\frac{2}{27}\qquad $tech: 2*3^(-3) $f(-2)=2(3^{-2})=\displaystyle \frac{2}{3^{2}}=\frac{2}{9}\qquad $tech: 2*3^(-2) $f(-1)=2(3^{-1})=\displaystyle \frac{2}{3^{1}}=\frac{2}{3}\qquad $tech: 2*3^(-1) $f(0)=2(3^{0})=2(1)=2\qquad $tech: 2*3^0 $f(1)=2(3^{1})=2(3)=6\qquad $tech: 2*3^1 $f(2)=2(3^{2})=2(9)=18\qquad $tech: 2*3^2 $f(3)=2(3^{3})=2(27)=54\qquad $tech: 2*3^3
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