Questions: The graphs, on the right, show the percentage of jobs in a country's labor force held by men and women from 1970 through 2015. The formula p=1.4 sqrt(t)+39 models the percentage of jobs in the labor force, p, held by women t years after 1970. Answer parts a through c. a. Use the appropriate graph to estimate the percentage of jobs in the labor force held by women in 2010. p=47 % b. Use the mathematical model to determine the percentage of jobs in the labor force held by women in 2010. p=47.9 % c. According to the formula, when will 53 % of jobs in the labor force be held by women? 53 % of jobs in the labor force will be held by women by 2024.

The graphs, on the right, show the percentage of jobs in a country's labor force held by men and women from 1970 through 2015. The formula p=1.4 sqrt(t)+39 models the percentage of jobs in the labor force, p, held by women t years after 1970. Answer parts a through c. a. Use the appropriate graph to estimate the percentage of jobs in the labor force held by women in 2010. p=47 % b. Use the mathematical model to determine the percentage of jobs in the labor force held by women in 2010. p=47.9 % c. According to the formula, when will 53 % of jobs in the labor force be held by women? 53 % of jobs in the labor force will be held by women by 2024.
Transcript text: The graphs, on the right, show the percentage of jobs in a country's labor force held by men and women from 1970 through 2015. The formula $p=1.4 \sqrt{t}+39$ models the percentage of jobs in the labor force, $p$, held by women $t$ years after 1970. Answer parts a through c. a. Use the appropriate graph to estimate the percentage of jobs in the labor force held by women in 2010. \[ p=47 \% \] b. Use the mathematical model to determine the percentage of jobs in the labor force held by women in 2010. \[ p=47.9 \% \] c. According to the formula, when will $53 \%$ of jobs in the labor force be held by women? $53 \%$ of jobs in the labor force will be held by women by 2024.
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Solution

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Solution Steps

Step 1: Estimate the percentage of jobs in the labor force held by women in 2010 using the graph

From the graph, the percentage of jobs held by women in 2010 is approximately 47%.

Step 2: Use the mathematical model to determine the percentage of jobs in the labor force held by women in 2010

The formula given is \( p = 1.4 \sqrt{t} + 39 \), where \( t \) is the number of years after 1970. For 2010, \( t = 2010 - 1970 = 40 \).

Substitute \( t = 40 \) into the formula: \[ p = 1.4 \sqrt{40} + 39 \] \[ p \approx 1.4 \times 6.32 + 39 \] \[ p \approx 8.85 + 39 \] \[ p \approx 47.85 \]

Rounding to the nearest tenth, \( p \approx 47.9 \).

Step 3: Determine the year when 53% of jobs in the labor force will be held by women

Set \( p = 53 \) in the formula and solve for \( t \): \[ 53 = 1.4 \sqrt{t} + 39 \] \[ 53 - 39 = 1.4 \sqrt{t} \] \[ 14 = 1.4 \sqrt{t} \] \[ \sqrt{t} = \frac{14}{1.4} \] \[ \sqrt{t} = 10 \] \[ t = 10^2 \] \[ t = 100 \]

The year is \( 1970 + 100 = 2070 \).

Final Answer

  1. The estimated percentage of jobs held by women in 2010 using the graph is 47%.
  2. The percentage of jobs held by women in 2010 using the mathematical model is approximately 47.9%.
  3. According to the formula, 53% of jobs in the labor force will be held by women in the year 2070.
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