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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.)

During the year 1933

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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

In which state 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 Indiana in 2010?

$105,620

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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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Real-world applications

In 2004, a school population was 1001. By 2008 the population had grown to 1697. Assume the population is changing linearly.

  1. How much did the population grow between the year 2004 and 2008?
  2. How long did it take the population to grow from 1001 students to 1697 students?
  3. What is the average population growth per year?
  4. What was the population in the year 2000?
  5. Find an equation for the population, P , of the school t years after 2000.
  6. Using your equation, predict the population of the school in 2011.

  1. 696 people
  2. 4 years
  3. 174 people per year
  4. 305 people
  5. P ( t ) = 305 + 174 t
  6. 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.

  1. How much did the population grow between the year 2003 and 2007?
  2. How long did it take the population to grow from 1431 people to 2134 people?
  3. What is the average population growth per year?
  4. What was the population in the year 2000?
  5. Find an equation for the population, P of the town t years after 2000.
  6. 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.

  1. Find a linear equation for the monthly cost of the cell plan as a function of x , the number of monthly minutes used.
  2. Interpret the slope and y -intercept of the equation.
  3. Use your equation to find the total monthly cost if 687 minutes are used.

  1. C ( x ) = 0.15 x + 10
  2. The flat monthly fee is $10 and there is an additional $0.15 fee for each additional minute used
  3. $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.

  1. Find a linear equation for the monthly cost of the data plan as a function of x , the number of MB used.
  2. Interpret the slope and y -intercept of the equation.
  3. 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.

  1. Find a formula for the moose population, P since 1990.
  2. What does your model predict the moose population to be in 2003?

  1. P ( t ) = 190 t + 4360
  2. 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.

  1. Find a formula for the owl population, P. Let the input be years since 2003.
  2. 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.

  1. Give a linear equation for the remaining federal helium reserves, R, in terms of t, the number of years since 2010.
  2. In 2015, what will the helium reserves be?
  3. If the rate of depletion doesn’t change, in what year will the Federal Helium Reserve be depleted?

  1. R ( t ) = 16 2.1 t
  2. 5.5 billion cubic feet
  3. 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:

  1. Give a linear equation for the remaining oil reserves, R, in terms of t, the number of years since now.
  2. Seven years from now, what will the oil reserves be?
  3. 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?

More than 133 minutes

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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?

$66,666.67

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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

a colony of bacteria is growing exponentially doubling in size every 100 minutes. how much minutes will it take for the colony of bacteria to triple in size
Divya Reply
what is the importance knowing the graph of circular functions?
Arabella Reply
can get some help basic precalculus
ismail Reply
What do you need help with?
Andrew
how to convert general to standard form with not perfect trinomial
Camalia Reply
can get some help inverse function
ismail
Rectangle coordinate
Asma Reply
how to find for x
Jhon Reply
it depends on the equation
Robert
whats a domain
mike Reply
The domain of a function is the set of all input on which the function is defined. For example all real numbers are the Domain of any Polynomial function.
Spiro
foci (–7,–17) and (–7,17), the absolute value of the differenceof the distances of any point from the foci is 24.
Churlene Reply
difference between calculus and pre calculus?
Asma Reply
give me an example of a problem so that I can practice answering
Jenefa Reply
x³+y³+z³=42
Robert
dont forget the cube in each variable ;)
Robert
of she solves that, well ... then she has a lot of computational force under her command ....
Walter
what is a function?
CJ Reply
I want to learn about the law of exponent
Quera Reply
explain this
Hinderson Reply
what is functions?
Angel Reply
A mathematical relation such that every input has only one out.
Spiro
yes..it is a relationo of orders pairs of sets one or more input that leads to a exactly one output.
Mubita
Is a rule that assigns to each element X in a set A exactly one element, called F(x), in a set B.
RichieRich
If the plane intersects the cone (either above or below) horizontally, what figure will be created?
Feemark Reply

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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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