Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.2 - Basics of Functions and Their Graphs - Exercise Set - Page 179: 104

Answer

a) (10,69) b) G(10) underestimates by 2%

Work Step by Step

(a) Let us consider the provided function, $G\left( x \right)=-0.01{{x}^{2}}+x+60$ We have to calculate $G\left( 10 \right)$; put $x=10$ in the function, $G\left( 10 \right)=\left( -0.01 \right){{\left( 10 \right)}^{2}}+10+60$ Now simplify it as, $\begin{align} & G\left( 10 \right)=\left( -0.01 \right){{\left( 10 \right)}^{2}}+10+60 \\ & =-1+10+60 \\ & =69 \end{align}$ So, the given function $G\left( x \right)=-0.01{{x}^{2}}+x+60$ represents the wage gap in percentage of x years after 1980. The function is evaluated as $G\left( 10 \right)=69$ for $x=10$ , which shows that the wage gap was 69% after 10 years after 1980. That is, the wage gap was 69% in 1990. In function notation, the point on the graph is represented by $\left( x,G\left( x \right) \right)$. Thus, the obtained value of $G\left( 10 \right)=69$ is represented as a point on the graph as $\left( 10,69 \right)$. (b) The value of $G\left( 10 \right)$ as calculated in part (a) is 69, which states that the wage gap was 69% in 1990. But the actual data represented in the provided bar graph shows that in 1990 the wage gap was 71%. Thus, the calculated value of $G\left( 10 \right)$ underestimates the actual data shown by bar graph by 2%.
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