Answer
\[55\]
Work Step by Step
The national diversity index of U.S. is modeled by the formula \[D=0.005{{x}^{2}}+0.55x+34\].
Here, \[D\]is national diversity index \[x\] years after \[1980\].
The national diversity index is to be found for year\[2010\], that is,\[30\] years after \[1980\].
Substitute \[30\] for \[x\] in the formula:
\[\begin{align}
& D=0.005{{\left( 30 \right)}^{2}}+0.55\left( 30 \right)+34 \\
& =0.005\left( 900 \right)+16.5+34 \\
& =4.5+16.5+34 \\
& =55
\end{align}\]
The national diversity index as calculated by the mathematical formula is same as depicted by the bar graph.
The national diversity index in year \[2010\]is \[55\], which is same as depicted by the bar graph.
