Answer
a) (30,81)
b) G(30) underestimates by 2%
Work Step by Step
(a)
Let us consider the provided function,
$G\left( x \right)=-0.01{{x}^{2}}+x+60$
Now, to calculate $G\left( 30 \right)$ put $x=30$ in the function,
$G\left( 30 \right)=\left( -0.01 \right){{\left( 30 \right)}^{2}}+30+60$
Again, simplify it as,
$\begin{align}
& G\left( 30 \right)=\left( -0.01 \right){{\left( 30 \right)}^{2}}+30+60 \\
& =-9+30+60 \\
& =81
\end{align}$
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 $G\left( 30 \right)=81$ for $x=30$ , which shows that the wage gap was 81% after 30 years after 1980. That is, the wage gap was 81% in 2010.
In function notation, the point on the graph is represented by $\left( x,G\left( x \right) \right)$.
Therefore, the obtained value of $G\left( 30 \right)=81$ is represented as a point on the graph as $\left( 30,81 \right)$.
(b)
The value of $G\left( 30 \right)$ as calculated in part (a) is 81, which states that the wage gap was 81% in 2010. But the actual data represented in the provided bar graph shows that in 2010 the wage gap was 83%.
Thus, the calculated value of $G\left( 30 \right)$ underestimates the actual data shown by bar graph by 2%.
