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 643: 61

Answer

$y=3.6742\left(0.9036^{x}\right)$

Work Step by Step

The exponential function we want has the form $y=Ab^{x}$. $\left[\begin{array}{ll} \text{point on} & \text{corresponding}\\ \text{the graph} & \text{equation}\\ (2,3) & 3=Ab^{2}\\ (6,2) & 2=Ab^{6} \end{array}\right]$ Dividing the equations, $\displaystyle \frac{2}{3}=\frac{Ab^{6}}{Ab^{2}}$ $\displaystyle \frac{2}{3}=b^{4}$, so $b=\displaystyle \left(\frac{2}{3}\right)^{1/4}\approx 0.9036$ Back-substituting into the second equation, $3=A(0.9036)^{2}$ $A=\displaystyle \frac{3}{(0.9036)^{2}}\approx 3.6742$ The model is $y=Ab^{x}=3.6742\left(0.9036^{x}\right)$ $y=3.6742\left(0.9036^{x}\right)$
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