GEOMETRY: ANNUAL SALARIES AND GENDER (PERFORMANCE TASK) ... CONTINUED...

⬛️ Step 5: ⬛️

◉ . Without using regression, write a system of equations that
model the number of bachelor degrees earned by men and women
in Springfield as a function of x, the number of years since 2000.
Show your work.

➜ Equation for Springfield’s men: ｟Attachment #1:
step-by-step solving｠.

➜ Equation for Springfield’s women: ｟Attachment #2:
step-by-step solving｠.

◉ . When, if ever, will the number of women earning bachelor
degrees equal the number of men earning bachelor degrees in
Springfield? Justify your answer using appropriate mathematics
vocabulary.

➜ It will never be equal. This is because of the y
intercept on the equations. Both of them have the same
slope but not the same y intercept so they will never
touch meaning they will never be equal.

⬛️ Step 5: ⬛️

◉ . Assuming a linear relationship between year and salaries by
gender, determine when the median annual salary for women will
exceed men. Justify your answer. Include in the discussion the
regression analysis you performed.

➜ It will take 152.46 years for the median annual salary
of a woman to exceed men. I know this because I took
the data from the table above and plugged it into a
linear regression calculator. I used the median annual
salary for both men and women as the y values and I
used the year from 2000 as the x value. I then
calculated the average income increase over the years
for both men and women and made it into 2 separate
linear equations. I then wrote the equation as having
them both equal to each other. This gave me the
solution -154.46. This means that in 154.46 years
women will make more than men on average.

◉ . Based on the answer you found in the above step, provide an
argument pro or con to the statement “As the number of women
exceed men in the number of bachelor degrees received, expect
there to be a corresponding change in the median annual salaries
for each gender.”

➜ Obviously this is true. With the statistic that women
have more bachelor degrees that means that they will
obviously be making more money than men. This
means women's median annual salaries will increase
faster than men's annual salary increase.