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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

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Find and interpret the y -intercept.

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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

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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 .

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

18,500

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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?

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

$91,625

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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
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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).

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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
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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.

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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.

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In what year will the percentage exceed 12%?

2023

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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
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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

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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

By the definition, is such that 0!=1.why?
Unikpel Reply
(1+cosA+IsinA)(1+cosB+isinB)/(cos@+isin@)(cos$+isin$)
Ajay Reply
hatdog
Mark
how we can draw three triangles of distinctly different shapes. All the angles will be cutt off each triangle and placed side by side with vertices touching
Shahid Reply
bsc F. y algebra and trigonometry pepper 2
Aditi Reply
given that x= 3/5 find sin 3x
Adamu Reply
4
DB
remove any signs and collect terms of -2(8a-3b-c)
Joeval Reply
-16a+6b+2c
Will
is that a real answer
Joeval
(x2-2x+8)-4(x2-3x+5)
Ayush Reply
sorry
Miranda
x²-2x+9-4x²+12x-20 -3x²+10x+11
Miranda
x²-2x+9-4x²+12x-20 -3x²+10x+11
Miranda
(X2-2X+8)-4(X2-3X+5)=0 ?
master
The anwser is imaginary number if you want to know The anwser of the expression you must arrange The expression and use quadratic formula To find the answer
master
The anwser is imaginary number if you want to know The anwser of the expression you must arrange The expression and use quadratic formula To find the answer
master
Y
master
X2-2X+8-4X2+12X-20=0 (X2-4X2)+(-2X+12X)+(-20+8)= 0 -3X2+10X-12=0 3X2-10X+12=0 Use quadratic formula To find the answer answer (5±Root11i)/3
master
Soo sorry (5±Root11* i)/3
master
x2-2x+8-4x2+12x-20 x2-4x2-2x+12x+8-20 -3x2+10x-12 now you can find the answer using quadratic
Mukhtar
2x²-6x+1=0
Ife
explain and give four example of hyperbolic function
Lukman Reply
What is the correct rational algebraic expression of the given "a fraction whose denominator is 10 more than the numerator y?
Racelle Reply
y/y+10
Mr
Find nth derivative of eax sin (bx + c).
Anurag Reply
Find area common to the parabola y2 = 4ax and x2 = 4ay.
Anurag
y2=4ax= y=4ax/2. y=2ax
akash
A rectangular garden is 25ft wide. if its area is 1125ft, what is the length of the garden
Jhovie Reply
to find the length I divide the area by the wide wich means 1125ft/25ft=45
Miranda
thanks
Jhovie
What do you call a relation where each element in the domain is related to only one value in the range by some rules?
Charmaine Reply
A banana.
Yaona
a function
Daniel
a function
emmanuel
given 4cot thither +3=0and 0°<thither <180° use a sketch to determine the value of the following a)cos thither
Snalo Reply
what are you up to?
Mark Reply
nothing up todat yet
Miranda
hi
jai
hello
jai
Miranda Drice
jai
aap konsi country se ho
jai
which language is that
Miranda
I am living in india
jai
good
Miranda
what is the formula for calculating algebraic
Propessor Reply
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
Miranda
Practice Key Terms 5

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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