Using data starting with 1950 and projected to​ 2050, the number of women​ (in millions) in the workforce is given by the function Upper P equals 0.79 x plus 20.86​, where x equals the number of years after 1950.

Question

​(a) Find the value of P when xequals37. Explain what this means.
​(b) What value of x represents 2030​? Use the model to find the number of women in the workforce in 2030.

Answer 1

Given the function for the number of women in the workforce, \( P = 0.79x + 20.86 \), where \( x \) is the number of years after 1950, let's address both parts of your question.

Part (a):

Find the value of \( P \) when \( x = 37 \).

To find \( P \) when \( x = 37 \): \[ P = 0.79(37) + 20.86 \]

Calculating \( 0.79 \times 37 \): \[ 0.79 \times 37 = 29.23 \]

Now, adding 20.86: \[ P = 29.23 + 20.86 = 50.09 \]

Interpretation: When \( x = 37 \), which corresponds to the year \( 1950 + 37 = 1987 \), the model predicts that there will be approximately 50.09 million women in the workforce.

Part (b):

What value of \( x \) represents 2030?

To find \( x \) for the year 2030: \[ x = 2030 - 1950 = 80 \]

Use the model to find the number of women in the workforce in 2030: \[ P = 0.79(80) + 20.86 \]

Calculating \( 0.79 \times 80 \): \[ 0.79 \times 80 = 63.2 \]

Now, adding 20.86: \[ P = 63.2 + 20.86 = 84.06 \]

Conclusion: The model predicts that in 2030, there will be approximately 84.06 million women in the workforce.