Precalculus (6th Edition) Blitzer

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

Chapter 2 - Section 2.6 - Rational Functions and Their Graphs - Exercise Set - Page 401: 107


a. $\frac{1.75x^2-15.9x+160}{2.1x^2-3.5x+296}$ b. $67\%$ c. $66\%$; underestimates by $1\%$ d. $y=\frac{5}{6}$, $83\ (\%)$

Work Step by Step

a. Using the given equations, we have $r(x)=\frac{p(x)}{q(x)}=\frac{1.75x^2-15.9x+160}{2.1x^2-3.5x+296}$ b. Using the given graph, in 2010, the ratio is $\frac{25040}{37207}\approx67\ (\%)$ c. For year 2010, $x=2010-1970=40$ Wwe have $r(40)=\frac{1.75(40)^2-15.9(40)+160}{2.1(40)^2-3.5(40)+296}\approx66\ (\%)$ . This underestimates the value by $1\%$ compared with the value from part-b. d. When $x\to\infty$, we have $r\to\frac{1.75}{2.1}=\frac{5}{6}$ Thus the asymptote is $y=\frac{5}{6}$. For a long time, the percentage will be $\frac{5}{6}\approx83\ (\%)$
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