<< Chapter < Page Chapter >> Page >
This graph shows profits starting at 1985 at $10,000 and ending at 2005 at $4,000.  The x-axis ranges from 0 to 30 in intervals of 5 and the y –axis goes from 0 to 12,000 in intervals of 2,000.

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

y = 3 00 x + 11 , 5 00

Got questions? Get instant answers now!

Find and interpret the y -intercept.

Got questions? Get instant answers now!

For the following exercise, consider this scenario: In 2004, a school population was 1,700. By 2012 the population had grown to 2,500.

Assume the population is changing linearly.

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

a) 800 b) 100 students per year c) P ( t ) = 1 00 t + 17 00

Got questions? Get instant answers now!

For the following exercises, consider this scenario: In 2000, the moose population in a park was measured to be 6,500. By 2010, the population was measured to be 12,500. Assume the population continues to change linearly.

Find a formula for the moose population, P .

Got questions? Get instant answers now!

What does your model predict the moose population to be in 2020?

18,500

Got questions? Get instant answers now!

For the following exercises, consider this scenario: The median home values in subdivisions Pima Central and East Valley (adjusted for inflation) are shown in [link] . Assume that the house values are changing linearly.

Year Pima Central East Valley
1970 32,000 120,250
2010 85,000 150,000

In which subdivision have home values increased at a higher rate?

Got questions? Get instant answers now!

If these trends were to continue, what would be the median home value in Pima Central in 2015?

$91,625

Got questions? Get instant answers now!

Fitting Linear Models to Data

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

0 2 4 6 8 10
–105 –50 1 55 105 160
Got questions? Get instant answers now!

Draw a scatter plot for the data in [link] . If we wanted to know when the population would reach 15,000, would the answer involve interpolation or extrapolation?

Year Population
1990 5,600
1995 5,950
2000 6,300
2005 6,600
2010 6,900

Extrapolation


Scatter plot with the points (1990,5600); (1995,5950); (2000,6300); (2005,6600); and (2010,6900).

Got questions? Get instant answers now!

Eight students were asked to estimate their score on a 10-point quiz. Their estimated and actual scores are given in [link] . Plot the points, then sketch a line that fits the data.

Predicted Actual
6 6
7 7
7 8
8 8
7 9
9 10
10 10
10 9
Got questions? Get instant answers now!

Draw a best-fit line for the plotted data.

Scatter plot of the points: (2,78); (4,81); (6,85); (8,90); and (10,99).


Scatter plot of: (2,78); (4,81); (6,85); (8,90); and (10,99) and the line of best fit running through these points.  The line of best fit goes through most of the points.

Got questions? Get instant answers now!

For the following exercises, consider the data in [link] , which shows the percent of unemployed in a city of people 25 years or older who are college graduates is given below, by year.

Year 2000 2002 2005 2007 2010
Percent Graduates 6.5 7.0 7.4 8.2 9.0

Determine whether the trend appears to be 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 exceed 12%?

2023

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 to three decimal places.

x 17 20 23 26 29
y 15 25 31 37 40
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 to three decimal places.

x 10 12 15 18 20
y 36 34 30 28 22

y = 1.294 x + 49.412 ;   r = 0.974

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

Questions & Answers

sin theta=3/4.prove that sec square theta barabar 1 + tan square theta by cosec square theta minus cos square theta
Umesh Reply
I want to know trigonometry but I can't understand it anyone who can help
Siyabonga Reply
Yh
Idowu
which part of trig?
Nyemba
functions
Siyabonga
trigonometry
Ganapathi
differentiation doubhts
Ganapathi
hi
Ganapathi
hello
Brittany
Prove that 4sin50-3tan 50=1
Sudip Reply
f(x)= 1 x    f(x)=1x  is shifted down 4 units and to the right 3 units.
Sebit Reply
f (x) = −3x + 5 and g (x) = x − 5 /−3
Sebit
what are real numbers
Marty Reply
I want to know partial fraction Decomposition.
Adama Reply
classes of function in mathematics
Yazidu Reply
divide y2_8y2+5y2/y2
Sumanth Reply
wish i knew calculus to understand what's going on 🙂
Dashawn Reply
@dashawn ... in simple terms, a derivative is the tangent line of the function. which gives the rate of change at that instant. to calculate. given f(x)==ax^n. then f'(x)=n*ax^n-1 . hope that help.
Christopher
thanks bro
Dashawn
maybe when i start calculus in a few months i won't be that lost 😎
Dashawn
what's the derivative of 4x^6
Axmed Reply
24x^5
James
10x
Axmed
24X^5
Taieb
Thanks for this helpfull app
Axmed Reply
secA+tanA=2√5,sinA=?
richa Reply
tan2a+tan2a=√3
Rahulkumar
classes of function
Yazidu
if sinx°=sin@, then @ is - ?
NAVJIT Reply
the value of tan15°•tan20°•tan70°•tan75° -
NAVJIT
0.037 than find sin and tan?
Jon Reply
cos24/25 then find sin and tan
Deepak Reply
Practice Key Terms 5

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

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

Ask