<< Chapter < Page Chapter >> Page >
x y
4 44.8
5 43.1
6 38.8
7 39
8 38
9 32.7
10 30.1
11 29.3
12 27
13 25.8
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x 21 25 30 31 40 50
y 17 11 2 –1 –18 –40

y = 1 . 981 x + 6 0. 197; r = 0. 998

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x y
100 2000
80 1798
60 1589
55 1580
40 1390
20 1202
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x 900 988 1000 1010 1200 1205
y 70 80 82 84 105 108

y = 0. 121 x 38.841 , r = 0.998

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Extensions

Graph f ( x ) = 0.5 x + 10. Pick a set of five ordered pairs using inputs x = −2 , 1 , 5 , 6 , 9 and use linear regression to verify that the function is a good fit for the data.

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Graph f ( x ) = 2 x 10. Pick a set of five ordered pairs using inputs x = −2 , 1 , 5 , 6 , 9 and use linear regression to verify the function.

( −2 , −6 ) , ( 1 , −12 ) , ( 5 , −20 ) , ( 6 , −22 ) , ( 9 , −28 ) ; Yes, the function is a good fit.

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For the following exercises, consider this scenario: The profit of a company decreased steadily over a ten-year span. The following ordered pairs shows 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 , 1 , 600 ) , ( 48 , 1 , 55 0 ) , ( 50 , 1 , 505 ) , ( 52 , 1 , 54 0 ) , ( 54 , 1 , 495 ) .

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

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Find to the nearest tenth and interpret the x -intercept.

( 189 .8 , 0 ) If 18,980 units are sold, the company will have a profit of zero dollars.

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Find to the nearest tenth and interpret the y -intercept.

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Real-world applications

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:

( 25 00 , 2000 ) , ( 265 0 , 2001 ) , ( 3000 , 2003 ) , ( 35 00 , 2006 ) , ( 42 00 , 2010 )

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

y = 0.00587 x + 1985 .4 1

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Predict when the population will hit 8,000.

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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 , 25 0 ) , ( 48 , 3 05 ) , ( 50 , 35 0 ) , ( 52 , 39 0 ) , ( 54 , 41 0 ) .

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 = 2 0. 25 x 671 . 5

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Predict when the profit will exceed one million dollars.

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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 , 25 0 ) , ( 48 , 225 ) , ( 50 , 2 05 ) , ( 52 , 18 0 ) , ( 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 = 1 0. 75 x + 742 . 5 0

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

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Chapter review exercises

Linear Functions

Determine whether the algebraic equation is linear. 2 x + 3 y = 7

Yes

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Questions & Answers

differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
what is labour ?
Lambiv
how will I do?
Venny Reply
how is the graph works?I don't fully understand
Rezat Reply
information
Eliyee
devaluation
Eliyee
t
WARKISA
hi guys good evening to all
Lambiv
multiple choice question
Aster Reply
appreciation
Eliyee
explain perfect market
Lindiwe Reply
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
yes,thank you
Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
ok
Shukri
how do you save a country economic situation when it's falling apart
Lilia Reply
what is the difference between economic growth and development
Fiker Reply
Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
Abdisa Reply
any question about economics?
Awais Reply
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
thank you so much 👍 sir
Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
Feyisa Reply
Answer
Feyisa
c
Jabir
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
Gsbwnw Reply
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
types of unemployment
Yomi Reply
What is the difference between perfect competition and monopolistic competition?
Mohammed
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Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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