For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs shows the population and the year over the ten-year span, (population, year) for specific recorded years:

(2500, 2000), (2650, 2001), (3000, 2003), (3500, 2006), (4200, 2010)
(2500, 2000), (2650, 2001), (3000, 2003), (3500, 2006), (4200, 2010)

Use linear regression to determine a function y,y, where the year depends on the population. Round to three decimal places of accuracy.

y=0.00587x+1985.41y=0.00587x+1985.41

Predict when the population will hit 8,000.

For the following exercises, consider this scenario: The profit of a company increased steadily over a ten-year span. The following ordered pairs show the number of units sold in hundreds and the profit in thousands of over the ten year span, (number of units sold, profit) for specific recorded years:

(46, 250), (48, 305), (50, 350), (52, 390), (54, 410)(46, 250), (48, 305), (50, 350), (52, 390), (54, 410).

Use linear regression to determine a function *y*, where the profit in thousands of dollars depends on the number of units sold in hundreds .

y=20.25x−671.5y=20.25x−671.5

Predict when the profit will exceed one million dollars.

For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs show dollars and the number of units sold in hundreds and the profit in thousands of over the ten-year span (number of units sold, profit) for specific recorded years:

(46, 250), (48, 225), (50, 205), (52, 180), (54, 165).
(46, 250), (48, 225), (50, 205), (52, 180), (54, 165).

Use linear regression to determine a function *y*, where the profit in thousands of dollars depends on the number of units sold in hundreds .

y=−10.75x+742.50y=−10.75x+742.50

Predict when the profit will dip below the $25,000 threshold.

AnalysisThis linear equation can then be used to approximate answers to various questions we might ask about the trend.