Answer
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 $90\%$.
