Let's take a detailed step-by-step approach to analyze the data presented in the table for births per 1000 people in South Africa over the listed years.
1. Identify the data points:
The table contains data on the rate of births per 1000 people in South Africa for specific years. The pairs of (year, birth rate) are:
- 2001: 25.4 births per 1000 people
- 2003: 24.6 births per 1000 people
- 2005: 23.7 births per 1000 people
- 2007: 22.8 births per 1000 people
- 2009: 21.8 births per 1000 people
- 2011: 20.9 births per 1000 people
2. Listing the years:
From the table, the years under consideration are:
[tex]\[
[2001, 2003, 2005, 2007, 2009, 2011]
\][/tex]
3. Listing the corresponding birth rates per 1000 people:
The corresponding birth rates for these years are:
[tex]\[
[25.4, 24.6, 23.7, 22.8, 21.8, 20.9]
\][/tex]
4. Observing the trend:
By observing the data, we can see that the number of births per 1000 people has been decreasing steadily over the listed years. Here's a breakdown:
[tex]\[
\begin{align*}
2001: & \ 25.4 \\
2003: & \ 24.6 \\
2005: & \ 23.7 \\
2007: & \ 22.8 \\
2009: & \ 21.8 \\
2011: & \ 20.9 \\
\end{align*}
\][/tex]
5. Summarizing the pattern:
- From 2001 to 2003, the rate decreased by [tex]\( 25.4 - 24.6 = 0.8 \)[/tex]
- From 2003 to 2005, the rate decreased by [tex]\( 24.6 - 23.7 = 0.9 \)[/tex]
- From 2005 to 2007, the rate decreased by [tex]\( 23.7 - 22.8 = 0.9 \)[/tex]
- From 2007 to 2009, the rate decreased by [tex]\( 22.8 - 21.8 = 1.0 \)[/tex]
- From 2009 to 2011, the rate decreased by [tex]\( 21.8 - 20.9 = 0.9 \)[/tex]
The pattern suggests a consistent decrease in the birth rate per 1000 people.
6. Conclusion:
The provided data shows a decreasing trend in the birth rates in South Africa over the span of a decade from 2001 to 2011. Birth rates dropped from 25.4 to 20.9 births per 1000 people.
Hence, the list of years is:
[tex]\[
[2001, 2003, 2005, 2007, 2009, 2011]
\][/tex]
And the corresponding birth rates per 1000 people are:
[tex]\[
[25.4, 24.6, 23.7, 22.8, 21.8, 20.9]
\][/tex]
