Calculus Concepts: An Informal Approach to the Mathematics of Change 5th Edition

Published by Brooks Cole
ISBN 10: 1-43904-957-2
ISBN 13: 978-1-43904-957-0

Chapter 1 - Ingredients of Change: Functions and Limits - 1.1 Activities - Page 11: 39


$a)$ The value of a $2001$ contastant dollar in $2000$ is $1.023$ and in $2010$ is $0.793$ $b)$ The model will fall to below $80$ cents in $2010$ and bellow $75$ cents in $2012$

Work Step by Step

$a)$ For this exercise we will just evaluate the value of the function when $t=-1$ and $t=9$ : $d(-1)=-0.023*(-1)+1.00=1.023$ $d(9)=-0.023*(9)+1.00=0.793$ $b)$ For this exercise, we will just solve the following inequality, $d(t)1.00-y⇔$ $⇔t>\frac{1.00-y}{0.023}$ For $y=0.80$ we have $t\approx8.696$ and for $y=0.75$ we have $t\approx10,869$. We can conclude from this that the model will fall to below $80$ cents in 2010 and below $75$ cents in 2012.
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