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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.
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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.
-
people
-
years
- Average rate of growth
people per year
So, using
we have
- The year 2000 corresponds to
So,
or roughly 904 people in year 2000
- If the year 2000 corresponds to
then we have ordered pair
corresponds to
- The year 2014 corresponds to
Therefore,
.
So, a population of 3364.
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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.
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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.
-
- 0.06 For every MB, the client is charged 6 cents.
If no usage occurs, the client is charged $10
-
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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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