Precalculus (6th Edition) Blitzer

a) The percentage value of the white adults is $92\%$. b) The year is $2027$.
(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 $90\%$.