9514 1404 393
Answer:
year 2066
Step-by-step explanation:
In order to do this, we need to make some assumptions. We'll assume that the 2010 wages are also in 2009 dollars. (If not, there's an inflation factor that needs to be accounted for.) We also need to assume the form of the change in wages over time. The simplest assumption there is that wages change linearly.
Then we can write equations for men's and women's wages as follows:
Using the 2-point form of the equation for a line, we have ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
<u>Men's wages</u>
y = (42800 -38907)/(2010-1960)(x -1960) +38907
y = 77.86(x -1960) +38907
y = 77.86x -113,698.6 . . . . . where x is the year
<u>Women's wages</u>
y = (34700 -23606)/(2010 -1960)(x -1960) +23606
y = 221.88x -411,278
These values are equal when ...
77.86x -113,698.6 = 221.88x -411,278
297,580.2 = 144.02x . . . . . . . add 411278 -77.86x
2066.2 = x . . . . . . . divide by the coefficient of x
Based on this data we predict women's wages might catch up to men's in the year 2066, about 56 years from 2010.
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<em>Alternate solution</em>
In the 50 years from 1960 to 2010, the fraction of men's wages that women receive has increased from 23606/38907 ≈ 0.606729 to 34700/42800 ≈ 0.810748. That is a change of about 0.204 of men's wages in 50 years. The remaining fraction of 1-0.810748 = 0.189 might be expected to be wiped out in another (0.189/0.204)(50 years) = 46.4 years. That would be the year 2056.
The different results come from different assumptions. For the second solution, we assumed that the fraction improved linearly. Under the first assumption, that wages improved linearly, the fractional improvement is non-linear, and decreases over time.
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<em>Additional comment</em>
The usual assumption regarding things financial is that they change exponentially over time. If we use an exponential model, instead of a linear one, wage parity is reached in about 2046.
