Answer:
Explanation:
To find the quadratic function that models the population, we can use quadratic regression. We can assign the variable x as the number of years after 1970, and y as the labor pool in millions of people. We can then input the data into a calculator or a spreadsheet software and use regression analysis to find the quadratic equation that best fits the data.
Using a spreadsheet software, we can input the data and use the trendline feature to find the quadratic function. The resulting equation is:
y = -32.917x^2 + 338.958x + 63.396
Therefore, the quadratic function that best models this population as a function of the number of years after 1970 is:
y = -32.917x^2 + 338.958x + 63.396
where x is the number of years after 1970 and y is the number of millions of people in this labor pool.
b. According to the model, what is the projected size of the labor pool in 2025?
To find the projected size of the labor pool in 2025, we need to plug in x = 55 (since 2025 is 55 years after 1970) into the quadratic function we found in part (a):
y = -32.917x^2 + 338.958x + 63.396
y = -32.917(55)^2 + 338.958(55) + 63.396
y = -32.917(3025) + 18642.19 + 63.396
y = -99588.508 + 18642.19 + 63.396
y = -80982.922
Rounding to the nearest million, we get a projected size of the labor pool in 2025 of 83 million. Therefore, according to the model, the projected size of the labor pool in 2025 is 83 million.