The problem involves using a linear function to estimate the number of women in the workforce based on the number of years since 1950. The given equation is $P = 0.79x + 20.86$, where $x$ is the number of years after 1950 and $P$ represents the number of women (in millions) in the workforce.

Let's solve the following parts:

(a) Find the value of $P$ when $x = 42$, and explain its meaning.

Using the equation $P = 0.79x + 20.86$: $P = 0.79(42) + 20.86$ Let's calculate this value first.

(b) What value of $x$ represents 2020, and find the number of women in the workforce in 2020.

To find $x$, subtract 1950 from 2020: $x = 2020 - 1950 = 70$ Now, calculate $P$ when $x = 70$ using the same equation.

I will calculate both (a) and (b) now.### (a) When $x = 42$, we find: $P = 54.04$ This means that in the year 1992 (since $1950 + 42 = 1992$), there were approximately 54.04 million women in the workforce.

(b) When $x = 70$ (representing the year 2020):

$P = 76.16$ This means that in the year 2020, there were approximately 76.16 million women in the workforce.

Would you like further clarifications on these calculations or more details?

Here are some related questions:

1. How would changes in the slope $0.79$ affect workforce predictions?
2. How can you interpret the value of 20.86 in the equation?
3. What if we wanted to predict for a year beyond 2050? What considerations are needed?
4. How accurate are linear models like this for long-term workforce predictions?
5. How does the workforce growth rate of women compare with other workforce segments?

Tip: Always check the domain of a model like this to ensure it's appropriate for your data range!