Sure, let's find the percentage change in the proportion of married Americans from 1970 to 2010.
1. Identify the initial and final values:
- Initial value (percentage in 1970): [tex]\( 71.70\% \)[/tex]
- Final value (percentage in 2010): [tex]\( 56.34\% \)[/tex]
2. Calculate the absolute change:
[tex]\[
\text{Absolute change} = \text{Final value} - \text{Initial value} = 56.34\% - 71.70\%
\][/tex]
3. Compute the difference:
[tex]\[
56.34\% - 71.70\% = -15.36\%
\][/tex]
4. Determine the percentage change relative to the initial value:
[tex]\[
\text{Percentage change} = \left( \frac{\text{Absolute change}}{\text{Initial value}} \right) \times 100
\][/tex]
Here, the absolute change is [tex]\(-15.36\%\)[/tex] and the initial value is [tex]\(71.70\%\)[/tex].
5. Plug in the values:
[tex]\[
\text{Percentage change} = \left( \frac{-15.36}{71.70} \right) \times 100
\][/tex]
6. Calculate the ratio:
[tex]\[
\frac{-15.36}{71.70} \approx -0.2142259
\][/tex]
7. Multiply by 100 to get the percentage change:
[tex]\[
-0.2142259 \times 100 \approx -21.42\%
\][/tex]
Hence, the percentage change in the proportion of married Americans from 1970 to 2010 is approximately [tex]\(-21.42\%\)[/tex]. This indicates a decrease of about 21.42%.
