Precalculus (6th Edition) Blitzer

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

Chapter 3 - Section 3.4 - Exponential and Logarithmic Equations - Exercise Set - Page 490: 116

Answer

a. $16.5\%$, overestimates $0.3\%$ b. $2017$

Work Step by Step

a. Given the model function $f (x) = 1.2 ln (x) + 15.7$, for year 2008, $x=2008-2006=2$, we have $f (2) = 1.2 ln (2) + 15.7\approx16.5$ percent. The bar graph gives a value of $16.2$ for year 2008; thus the model result overestimates the data by $0.3\%$ b. Letting $f(x)=18.6\%$, we have $ 1.2 ln (x) + 15.7=18.6$, which gives $ln(x)\approx2.4167$ and $x\approx11\ yrs$, corresponding to year $2006+11=2017$
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