Question

The given bar graph shows the percentage of U.S. women in the labor force from 1960 through 2010. The function f left parenthesis x right parenthesis equals 3.5 square root of x plus 38 models the percentage of U.S. women in the labor force, f left parenthesis x right parenthesis , x years after 1960. Use this formula to solve the following questions.

US women in Labor Force

According to the model, when will 70% of the U.S. women participate in the work force? Show all work and explain your answer in the context of the problem.

Answer 1

Half of year 2043

Explanation:

The function is: f(x) = 3.5√x + 38

where f(x) represents the percentage of U.S. women in the labor force x years after 1960.

Replacing f(x) = 70 and isolating x, we get:

70 = 3.5√x + 38

3.5√x = 70 - 38

√x = 32/3.5

x = 9.14²

x = 83.5

This means, in year 1960 + 83.5 = 2043.5, that is, at half of year 2043