<< Chapter < Page Chapter >> Page >

(3,600, 2000); (4,000, 2001); (4,700, 2003); (6,000, 2006)

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

Got questions? Get instant answers now!

Predict when the population will hit 12,000.

Early in 2022

Got questions? Get instant answers now!

What is the correlation coefficient for this model to three decimal places of accuracy?

Got questions? Get instant answers now!

According to the model, what is the population in 2014?

7,660

Got questions? Get instant answers now!

Practice test

Determine whether the following algebraic equation can be written as a linear function. 2 x + 3 y = 7

Yes.

Got questions? Get instant answers now!

Determine whether the following function is increasing or decreasing. f ( x ) = 2 x + 5

Got questions? Get instant answers now!

Determine whether the following function is increasing or decreasing. f ( x ) = 7 x + 9

Increasing

Got questions? Get instant answers now!

Given the following set of information, find a linear equation satisfying the conditions, if possible.

Passes through (5, 1) and (3, –9)

Got questions? Get instant answers now!

Given the following set of information, find a linear equation satisfying the conditions, if possible.

x intercept at (–4, 0) and y -intercept at (0, –6)

y = −1.5 x 6

Got questions? Get instant answers now!

Find the slope of the line in [link] .

Got questions? Get instant answers now!

Write an equation for line in [link] .

y = 2 x 1

Got questions? Get instant answers now!

Does [link] represent a linear function? If so, find a linear equation that models the data.

x –6 0 2 4
g ( x ) 14 32 38 44
Got questions? Get instant answers now!

Does [link] represent a linear function? If so, find a linear equation that models the data.

x 1 3 7 11
g ( x ) 4 9 19 12

No.

Got questions? Get instant answers now!

At 6 am, an online company has sold 120 items that day. If the company sells an average of 30 items per hour for the remainder of the day, write an expression to represent the number of items that were sold n after 6 am.

Got questions? Get instant answers now!

For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular:

y = 3 4 x 9 4 x 3 y = 8

Perpendicular

Got questions? Get instant answers now!

2 x + y = 3 3 x + 3 2 y = 5

Got questions? Get instant answers now!

Find the x - and y -intercepts of the equation 2 x + 7 y = 14.

( 7 , 0 ) ; ( 0 , 2 )

Got questions? Get instant answers now!

Given below are descriptions of two lines. Find the slopes of Line 1 and Line 2. Is the pair of lines parallel, perpendicular, or neither?

Line 1: Passes through ( −2 , −6 ) and ( 3 , 14 )

Line 2: Passes through ( 2 , 6 ) and ( 4 , 14 )

Got questions? Get instant answers now!

Write an equation for a line perpendicular to f ( x ) = 4 x + 3 and passing through the point ( 8 , 10 ) .

y = 0.25 x + 12

Got questions? Get instant answers now!

Sketch a line with a y -intercept of ( 0 , 5 ) and slope 5 2 .

Got questions? Get instant answers now!

Graph of the linear function f ( x ) = −x + 6 .

Got questions? Get instant answers now!

For the two linear functions, find the point of intersection: x = y + 2 2 x 3 y = −1

Got questions? Get instant answers now!

A car rental company offers two plans for renting a car.

  • Plan A: $25 per day and $0.10 per mile
  • Plan B: $40 per day with free unlimited mileage

How many miles would you need to drive for plan B to save you money?

150

Got questions? Get instant answers now!

Find the area of a triangle bounded by the y axis, the line f ( x ) = 12 4 x , and the line perpendicular to f that passes through the origin.

Got questions? Get instant answers now!

A town’s population increases at a constant rate. In 2010 the population was 65,000. By 2012 the population had increased to 90,000. Assuming this trend continues, predict the population in 2018.

165,000

Got questions? Get instant answers now!

The number of people afflicted with the common cold in the winter months dropped steadily by 25 each year since 2002 until 2012. In 2002, 8,040 people were inflicted. Find the linear function that models the number of people afflicted with the common cold C as a function of the year, t . When will less than 6,000 people be afflicted?

Got questions? Get instant answers now!

For the following exercises, use the graph in [link] , showing the profit, y , in thousands of dollars, of a company in a given year, x , where x represents years since 1980.

Find the linear function y , where y depends on x , the number of years since 1980.

y = 875 x + 10 , 675

Got questions? Get instant answers now!

Find and interpret the y -intercept.

Got questions? Get instant answers now!

In 2004, a school population was 1250. By 2012 the population had dropped to 875. Assume the population is changing linearly.

  1. How much did the population drop between the year 2004 and 2012?
  2. What is the average population decline per year?
  3. Find an equation for the population, P , of the school t years after 2004.

  • a) 375
  • b) dropped an average of 46.875, or about 47 people per year
  • c) y = 46.875 t + 1250

Got questions? Get instant answers now!

Draw a scatter plot for the data provided in [link] . Then determine whether the data appears to be linearly related.

0 2 4 6 8 10
–450 –200 10 265 500 755
Got questions? Get instant answers now!

Draw a best-fit line for the plotted data.

Got questions? Get instant answers now!

For the following exercises, use [link] , which shows the percent of unemployed persons 25 years or older who are college graduates in a particular city, by year.

Year Percent Graduates
2000 8.5
2002 8.0
2005 7.2
2007 6.7
2010 6.4

Determine whether the trend appears linear. If so, and assuming the trend continues, find a linear regression model to predict the percent of unemployed in a given year to three decimal places.

Got questions? Get instant answers now!

In what year will the percentage drop below 4%?

Early in 2018

Got questions? Get instant answers now!

Based on the set of data given in [link] , calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient. Round to three decimal places of accuracy.

x 16 18 20 24 26
y 106 110 115 120 125
Got questions? Get instant answers now!

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 (in hundreds) and the year over the ten-year span, (population, year) for specific recorded years:

(4,500, 2000); (4,700, 2001); (5,200, 2003); (5,800, 2006)

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

y = 0.00455 x + 1979.5

Got questions? Get instant answers now!

Predict when the population will hit 20,000.

Got questions? Get instant answers now!

What is the correlation coefficient for this model?

r = 0.999

Got questions? Get instant answers now!
Practice Key Terms 5

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Precalculus' conversation and receive update notifications?

Ask