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.

What is the meaning of this value of​ P?
A.
The value of P represents the number of women in the workforce in the year 1997.
B.
The value of P represents the number of women who will join the work force between the years 1900 and 1947.
C.
The value of P represents the number of women who will join the work force between the years 1950 and 1997.
D.
The value of P represents the number of women in the workforce in the year 1947.

1 answer

To understand the meaning of the function \( P = 0.79x + 20.86 \), we need to clarify what \( x \) represents. Here, \( x \) is defined as the number of years after 1950.

We can analyze the options:

A. The value of \( P \) represents the number of women in the workforce in the year 1997.

  • To find the value of \( x \) for 1997, we calculate \( x = 1997 - 1950 = 47 \).
  • Plugging this into the function gives \( P = 0.79(47) + 20.86 = 37.03 \) million women. This option might not directly represent the specific number for that year unless we confirm the accuracy of the range.

B. The value of \( P \) represents the number of women who will join the workforce between the years 1900 and 1947.

  • This is incorrect because the function is applicable only for years starting from 1950.

C. The value of \( P \) represents the number of women who will join the workforce between the years 1950 and 1997.

  • This is also incorrect, as the function \( P \) gives the total number of women in the workforce, not just those joining.

D. The value of \( P \) represents the number of women in the workforce in the year 1947.

  • This is incorrect because \( P \) is defined only for years starting from 1950 and does not apply to 1947.

Based on the analysis, none of the options perfectly match the meaning of \( P \) as defined by the function. However, if we look closely, option A comes most closely to reflecting a specific year (1997) even if it isn't stated directly.

Thus, A is the best choice.