To analyze the function \( P = 0.79x + 20.86 \), where \( x \) is the number of years after 1950, we can interpret \( P \) as the number of women (in millions) in the workforce for a given year.
Let's break down the possible interpretations of \( P \):
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If \( x = 0 \) (which corresponds to the year 1950): \[ P = 0.79(0) + 20.86 = 20.86 \text{ million women} \]
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If \( x = 47 \) (which corresponds to the year 1997): \[ P = 0.79(47) + 20.86 = 37.10 + 20.86 = 57.96 \text{ million women} \]
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If \( x = -3 \) (which would correspond to the year 1947): \[ P = 0.79(-3) + 20.86 = -2.37 + 20.86 = 18.49 \text{ million women} \]
Now we can evaluate the options provided:
A. The value of P represents the number of women in the workforce in the year 1997.
- This is true when \( x = 47 \), though the statement does not specify this, often implying general use of \( P \).
B. The value of P represents the number of women who will join the work force between the years 1900 and 1947.
- This is incorrect, as the model applies to 1950 and onwards.
C. The value of P represents the number of women who will join the workforce between the years 1950 and 1997.
- This is misleading; \( P \) does not indicate new entrants but total workforce participation at any given time.
D. The value of P represents the number of women in the workforce in the year 1947.
- This is incorrect, as it aligns with a year before the model's range (1950 onwards).
Given these explanations, the best interpretation of the value of \( P \) would be most aligned with A, as it discusses a future year (1997) in which the model can be correctly applied. However, it's important to note that the function itself denotes total numbers, not just new entrants.
Thus, the most correct option among the choices provided is A.