Question

According to data from the U.S Census Bureau, the total number of people in the United States labor force can be approximated by the function T(x) = –0.011x² + 2x + 107, where x is the number of years since 1980 and T(x) is the number of workers in millions. The number of women in the United States labor force can be approximated by the function W(x) = –0.012x² + 1.26x + 45.5. Write a polynomial function M(x) that models the number of men in the labor force and estimate the number of men in the labor force in 2008.

Answer 1

The polynomial function M(x) that models the number of men in the labor force is -0.001x² + 0.74x + 61.5. The estimated number of men in the labor force in 2008 is approximately 81.436 million.

Step-by-step explanation:

To find the polynomial function M(x) that models the number of men in the labor force, we need to subtract the number of women from the total number of people in the labor force. We can use the given functions T(x) and W(x) to do this. Let's start by subtracting W(x) from T(x) to get M(x):

M(x) = T(x) - W(x)

M(x) = (-0.011x² + 2x + 107) - (-0.012x² + 1.26x + 45.5)

M(x) = -0.011x² + 2x + 107 + 0.012x² - 1.26x - 45.5

M(x) = -0.001x² + 0.74x + 61.5

Now we can use the M(x) function to estimate the number of men in the labor force in 2008. Given that x is the number of years since 1980, we can substitute x = 2008 - 1980 = 28 into the M(x) function:

M(28) = -0.001(28)² + 0.74(28) + 61.5

M(28) = -0.001(784) + 20.72 + 61.5

M(28) = -0.784 + 20.72 + 61.5

M(28) ≈ 81.436

Therefore, the estimated number of men in the labor force in 2008 is approximately 81.436 million.