Questions: Use the following data from the Centers for Disease Control and Prevention to answer the following questions. Birth Year Male Life Expectancy Birth Year Female Life Expectancy --- --- --- --- 1970 67.4 1970 73.8 1980 69.1 1980 77.9 1990 73.1 1990 79.3 2000 73.9 2000 80.6 2010 76.3 2010 80.9

Use the following data from the Centers for Disease Control and Prevention to answer the following questions. Birth Year Male Life Expectancy Birth Year Female Life Expectancy --- --- --- --- 1970 67.4 1970 73.8 1980 69.1 1980 77.9 1990 73.1 1990 79.3 2000 73.9 2000 80.6 2010 76.3 2010 80.9
Transcript text: Use the following data from the Centers for Disease Control and Prevention to answer the following questions. \begin{tabular}{|cc|cc|} \hline \begin{tabular}{lc} Birth \\ Year \end{tabular} & \begin{tabular}{c} Male Life \\ Expectancy \end{tabular} & Birth Year & \begin{tabular}{c} Female Life \\ Expectancy \end{tabular} \\ \hline 1970 & 67.4 & 1970 & 73.8 \\ 1980 & 69.1 & 1980 & 77.9 \\ 1990 & 73.1 & 1990 & 79.3 \\ 2000 & 73.9 & 2000 & 80.6 \\ 2010 & 76.3 & 2010 & 80.9 \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Identify the Data

The table provides life expectancy data for males and females for the years 1970, 1980, 1990, 2000, and 2010.

Step 2: Calculate the Rate of Increase for Males
  • 1970 to 1980: \(69.1 - 67.4 = 1.7\)
  • 1980 to 1990: \(71.8 - 69.1 = 2.7\)
  • 1990 to 2000: \(73.9 - 71.8 = 2.1\)
  • 2000 to 2010: \(76.3 - 73.9 = 2.4\)

Average increase per decade for males: \((1.7 + 2.7 + 2.1 + 2.4) / 4 = 2.225\)

Step 3: Calculate the Rate of Increase for Females
  • 1970 to 1980: \(77.9 - 73.8 = 4.1\)
  • 1980 to 1990: \(79.3 - 77.9 = 1.4\)
  • 1990 to 2000: \(80.6 - 79.3 = 1.3\)
  • 2000 to 2010: \(80.9 - 80.6 = 0.3\)

Average increase per decade for females: \((4.1 + 1.4 + 1.3 + 0.3) / 4 = 1.775\)

Final Answer

  • Life expectancy is increasing faster for which group?

    • Answer: Males (2.225 > 1.775)

  • Assuming the trend continues, for what birth year are life expectancies equal?

    • To find the year when life expectancies are equal, we need to set up an equation based on the rates of increase:

      • Let \( x \) be the number of decades after 2010 when life expectancies are equal.
      • \( 76.3 + 2.225x = 80.9 + 1.775x \)
      • Solving for \( x \):
        • \( 76.3 + 2.225x = 80.9 + 1.775x \)
        • \( 2.225x - 1.775x = 80.9 - 76.3 \)
        • \( 0.45x = 4.6 \)
        • \( x = 4.6 / 0.45 \)
        • \( x \approx 10.22 \)
      • Adding 10.22 decades (102.2 years) to 2010:
        • \( 2010 + 102.2 \approx 2112 \)

    • Answer: 2112

  • What is the life expectancy for that year?

    • Using the male life expectancy formula:

      • \( 76.3 + 2.225 \times 10.22 \approx 76.3 + 22.74 \approx 99 \)

    • Answer: 99

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