The percentage of working mothers y can be modeled by the equation y=0.0102x + 0.644 where x is the number of years since 1990. In what year will 90% of mothers be in the labor force?
it is given that 'y' is 90%
rewriting the equation using this value gives 0.9 = 0.0102x + 0.644
now simply solve for x
To find the year when 90% of mothers will be in the labor force, we need to solve the equation:
y = 0.0102x + 0.644
We know that y represents the percentage of working mothers, and we want to find the year (x) when y is equal to 90%.
Let's substitute 90% (which is equal to 0.90) for y in the equation:
0.90 = 0.0102x + 0.644
Now we can solve this equation for x, which represents the number of years since 1990:
0.0102x = 0.90 - 0.644
0.0102x = 0.256
To isolate x, we divide both sides of the equation by 0.0102:
x = 0.256 / 0.0102
x ≈ 25.1
Since x represents the number of years since 1990, we can add 1990 to x to determine the year:
1990 + 25.1 ≈ 2015.1
Therefore, in approximately the year 2015, we can expect 90% of mothers to be in the labor force.