To analyze the given problem, let's start by breaking down each part step by step.
Given the function for the number of women in the workforce (in millions):
\[ P = 0.79x + 20.86 \]
where \( x \) represents the number of years after 1950.
(a) Find the value of \( P \) when \( x = 47 \).
To find \( P \) at \( x = 47 \):
\[ P = 0.79(47) + 20.86 \] \[ P = 37.13 + 20.86 \] \[ P = 57.99 \]
Therefore, when \( x = 47 \), the value of \( P \) is approximately 58 million women in the workforce.
Explanation: This means that in the year \( 1950 + 47 = 1997 \), there were about 58 million women in the workforce.
(b) What value of \( x \) represents 2020? Use the model to find the number of women in the workforce in 2020.
To find \( x \) for the year 2020:
\[ x = 2020 - 1950 = 70 \]
Now, we substitute \( x = 70 \) into the function to find \( P \):
\[ P = 0.79(70) + 20.86 \] \[ P = 55.3 + 20.86 \] \[ P = 76.16 \]
Therefore, in 2020, the model predicts approximately 76.16 million women in the workforce.
Summary:
- In 1997, there were about 58 million women in the workforce.
- In 2020, the model predicts around 76.16 million women in the workforce.
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