Precalculus (6th Edition) Blitzer

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

Chapter 3 - Review Exercises - Page 514: 82


a) The percentage value of the white adults is $92\%$. b) The year is $2027$.

Work Step by Step

(a) Let us consider the function of the white adults $ W\left( x \right)=11\ln x+49$ Calculate the percentage of students who completed their high school in 2012 as follows: The value of the total number of years from 1961 to 2012 is 51 years. So, substitute $ x=51$. Thus, $\begin{align} & W\left( x \right)=11\ln x+49 \\ & W\left( 51 \right)=11\ln \left( 51 \right)+49 \\ & =92 percent \end{align}$ Therefore, the resultant percentage of the white adults is $92\%$. (b) Let us consider the function of the black adults as follows: $ B\left( x \right)=16\ln x+23$ Calculate the year when percentage is $90\%$. Put $ B\left( x \right)=90$ So, $\begin{align} & B\left( x \right)=16\ln x+23 \\ & 90=16\ln x+23 \\ & \ln x=\frac{90-23}{16} \\ & =4.1875 \end{align}$ Thus, $\begin{align} & \ln x=4.1875 \\ & {{e}^{\ln x}}={{e}^{4.1875}} \\ & x=66 \end{align}$ So the year is $1961+66=2027$ In the year 2027, the percentage of black adults is $90\%$.
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