Answer
a) (10,69)
b) G(10) underestimates by 2%
Work Step by Step
(a)
Let us consider the provided function,
$G\left( x \right)=-0.01{{x}^{2}}+x+60$
We have to calculate $G\left( 10 \right)$; put $x=10$ in the function,
$G\left( 10 \right)=\left( -0.01 \right){{\left( 10 \right)}^{2}}+10+60$
Now simplify it as,
$\begin{align}
& G\left( 10 \right)=\left( -0.01 \right){{\left( 10 \right)}^{2}}+10+60 \\
& =-1+10+60 \\
& =69
\end{align}$
So, the given function $G\left( x \right)=-0.01{{x}^{2}}+x+60$ represents the wage gap in percentage of x years after 1980.
The function is evaluated as $G\left( 10 \right)=69$ for $x=10$ , which shows that the wage gap was 69% after 10 years after 1980. That is, the wage gap was 69% in 1990.
In function notation, the point on the graph is represented by $\left( x,G\left( x \right) \right)$.
Thus, the obtained value of $G\left( 10 \right)=69$ is represented as a point on the graph as $\left( 10,69 \right)$.
(b)
The value of $G\left( 10 \right)$ as calculated in part (a) is 69, which states that the wage gap was 69% in 1990. But the actual data represented in the provided bar graph shows that in 1990 the wage gap was 71%.
Thus, the calculated value of $G\left( 10 \right)$ underestimates the actual data shown by bar graph by 2%.