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If we assume the linear trend existed before 1950 and continues after 2000, the two states’ median house values will be (or were) equal in what year? (The answer might be absurd.)
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For the following exercises, use the median home values in Indiana and Alabama (adjusted for inflation) shown in
[link] . Assume that the house values are changing linearly.
Year |
Indiana |
Alabama |
1950 |
$37,700 |
$27,100 |
2000 |
$94,300 |
$85,100 |
If we assume the linear trend existed before 1950 and continues after 2000, the two states’ median house values will be (or were) equal in what year? (The answer might be absurd.)
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Real-world applications
In 2004, a school population was 1001. By 2008 the population had grown to 1697. Assume the population is changing linearly.
- How much did the population grow between the year 2004 and 2008?
- How long did it take the population to grow from 1001 students to 1697 students?
- What is the average population growth per year?
- What was the population in the year 2000?
- Find an equation for the population,
of the school
t years after 2000.
- Using your equation, predict the population of the school in 2011.
- 696 people
- 4 years
- 174 people per year
- 305 people
-
- 2219 people
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In 2003, a town’s population was 1431. By 2007 the population had grown to 2134. Assume the population is changing linearly.
- How much did the population grow between the year 2003 and 2007?
- How long did it take the population to grow from 1431 people to 2134 people?
- What is the average population growth per year?
- What was the population in the year 2000?
- Find an equation for the population,
of the town
years after 2000.
- Using your equation, predict the population of the town in 2014.
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A phone company has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 410 minutes, the monthly cost will be $71.50. If the customer uses 720 minutes, the monthly cost will be $118.
- Find a linear equation for the monthly cost of the cell plan as a function of
x , the number of monthly minutes used.
- Interpret the slope and
y -intercept of the equation.
- Use your equation to find the total monthly cost if 687 minutes are used.
-
- The flat monthly fee is $10 and there is an additional $0.15 fee for each additional minute used
- $113.05
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A phone company has a monthly cellular data plan where a customer pays a flat monthly fee of $10 and then a certain amount of money per megabyte (MB) of data used on the phone. If a customer uses 20 MB, the monthly cost will be $11.20. If the customer uses 130 MB, the monthly cost will be $17.80.
- Find a linear equation for the monthly cost of the data plan as a function of
, the number of MB used.
- Interpret the slope and
y -intercept of the equation.
- Use your equation to find the total monthly cost if 250 MB are used.
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In 1991, the moose population in a park was measured to be 4,360. By 1999, the population was measured again to be 5,880. Assume the population continues to change linearly.
- Find a formula for the moose population,
P since 1990.
- What does your model predict the moose population to be in 2003?
-
- 6640 moose
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In 2003, the owl population in a park was measured to be 340. By 2007, the population was measured again to be 285. The population changes linearly. Let the input be years since 1990.
- Find a formula for the owl population,
Let the input be years since 2003.
- What does your model predict the owl population to be in 2012?
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The Federal Helium Reserve held about 16 billion cubic feet of helium in 2010 and is being depleted by about 2.1 billion cubic feet each year.
- Give a linear equation for the remaining federal helium reserves,
in terms of
the number of years since 2010.
- In 2015, what will the helium reserves be?
- If the rate of depletion doesn’t change, in what year will the Federal Helium Reserve be depleted?
-
- 5.5 billion cubic feet
- During the year 2017
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Suppose the world’s oil reserves in 2014 are 1,820 billion barrels. If, on average, the total reserves are decreasing by 25 billion barrels of oil each year:
- Give a linear equation for the remaining oil reserves,
in terms of
the number of years since now.
- Seven years from now, what will the oil reserves be?
- If the rate at which the reserves are decreasing is constant, when will the world’s oil reserves be depleted?
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You are choosing between two different prepaid cell phone plans. The first plan charges a rate of 26 cents per minute. The second plan charges a monthly fee of $19.95
plus 11 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable?
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You are choosing between two different window washing companies. The first charges $5 per window. The second charges a base fee of $40 plus $3 per window. How many windows would you need to have for the second company to be preferable?
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When hired at a new job selling jewelry, you are given two pay options:
- Option A: Base salary of $17,000 a year with a commission of 12% of your sales
- Option B: Base salary of $20,000 a year with a commission of 5% of your sales
How much jewelry would you need to sell for option A to produce a larger income?
More than $42,857.14 worth of jewelry
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When hired at a new job selling electronics, you are given two pay options:
- Option A: Base salary of $14,000 a year with a commission of 10% of your sales
- Option B: Base salary of $19,000 a year with a commission of 4% of your sales
How much electronics would you need to sell for option A to produce a larger income?
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When hired at a new job selling electronics, you are given two pay options:
- Option A: Base salary of $20,000 a year with a commission of 12% of your sales
- Option B: Base salary of $26,000 a year with a commission of 3% of your sales
How much electronics would you need to sell for option A to produce a larger income?
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When hired at a new job selling electronics, you are given two pay options:
- Option A: Base salary of $10,000 a year with a commission of 9% of your sales
- Option B: Base salary of $20,000 a year with a commission of 4% of your sales
How much electronics would you need to sell for option A to produce a larger income?
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Questions & Answers
differentiate between demand and supply
giving examples
differentiated between demand and supply using examples
Lambiv
how is the graph works?I don't fully understand
hi guys good evening to all
Lambiv
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
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
Can I ask you other question?
Shukri
What is different between quantity demand and demand?
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
how do you save a country economic situation when it's falling apart
what is the difference between economic growth and development
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 ?
any question about economics?
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 .
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
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
What is the difference between perfect competition and monopolistic competition?
Mohammed
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Source:
OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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