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 - 1.4 Activities: 1

Answer

A) $.3$ B) The cost to rent a newly released movie increases value by $30$ cents for every year since $2010$. C) The cost to rent a newly released movie in $2010$ is $5$ dollars.

Work Step by Step

A) In the function $f(x)=ax+b$, the slope is defined by the $a$ value, which in this example is $.3$. B) The rate of change in this function can be represented by $(.3(x+1)+5)-(.3(x)+5)$. Solve this expression by doing $(.3x+.3+5)-(.3x+5)=.3$ This is the amount that is added to the cost for every year since $2010$. Rewrite this as "the cost to rent a newly released movie increases value by $30$ cents for every year since $2010$". C) If $f(x)=.3x+5$, then $f(0)=.3(0)+5=0+5=5$. To translate this, $0$ years since $2010$ is $2010$, and the cost to rent a newly released movie is $5$ dollars. Rewrite this as "the cost to rent a newly released movie in $2010$ is $5$ dollars".
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