Question

The size of the civilian labor force (in millions) for selected years from 1950 and projected to 2050 can be modeled by y= -0.0001x³ +0.0058x² +1.43x + 56.7, where x is the number of years after 1950.

(a) What does this model project the civilian labor force to be in 2013?
(b) In what year does the model project the civilian labor force to be 154 million?

Answer 1

Using the given model, the projected civilian labor force in 2013 is approximately 155.45 million. To determine the year when the labor force is projected to be 154 million, numerical methods or graphing techniques would be used to solve the cubic equation provided by the formula.

To find the projected civilian labor force in 2013 using the model y = -0.0001x³ + 0.0058x² + 1.43x + 56.7, where x is the number of years after 1950, we first calculate the value of x for 2013: x = 2013 - 1950 = 63. Plugging this into our model, we get:

y = -0.0001(63)³ + 0.0058(63)² + 1.43(63) + 56.7.

Performing the calculations:

y = -0.0001(250047) + 0.0058(3969) + 90.09 + 56.7 ≈ 155.45 million.

To find when the model projects the civilian labor force to be 154 million, we set y to 154 and solve the following equation:

154 = -0.0001x³ + 0.0058x² + 1.43x + 56.7.

This would typically be solved using numerical methods or graphing techniques as it is a cubic equation which might not have an algebraic solution.