## Related questions with answers

What is the chance that the next person I meet will be different from me? The diversity index, from 0 (no diversity) to 100, measures the chance that two randomly selected people are of a different race or ethnicity. The diversity index in the United States varies widely from region to region, from as high as 81 in Hawaii to as low as 11 in Vermont. The bar graph at the top of the next column shows the national diversity index for the United States for four years the period from 1980 through 2010.

The data in the graph can be modeled by the formula

$D=0.7 x+34 \text {, }$

where $D$ is the national diversity index for the United States $x$ years after 1980.

How well does the formula model the national diversity index for 2010?

Solutions

Verified$D=0.7x+34$

Where $D$ is the National diversity index for the USA.

For 2010, $x=2010-1980=30$

$\begin{aligned} D&=0.7x+34 \\ &=0.7 \times 30 +34 &\text{...Substitute in the values}\\ &= 21+34 &\text{...Multiply}\\ &=55 &\text{...Add} \end{aligned}$

From the chart also the index value in $55$ in $2010$. So the formula model holdes well (exact) for the naional diversity index of united states in $2010.$

$D=0.7x+34$

Where $D$ is the National diversity index for USA.

For $2010$, $x=2010-1980=30$

$\begin{align*} D&=0.7x+34\\ &=0.7 \times 30+ 34&\textcolor{#4257b2}{\text{...Substitute in the values}}\\ &=21+34&\textcolor{#4257b2}{\text{...Multiply}}\\ &=55&\textcolor{#4257b2}{\text{...Add}} \end{align*}$

From the chart also the index value is $55$ in $2010$. So the formula model holds well (exact) for the national diversity index of united states in $2010$.

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