-
Home
- Precalculus
- Linear functions
- Modeling with linear functions
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.)
Got questions? Get instant answers now!
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.)
Got questions? Get instant answers now!
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
Got questions? Get instant answers now!
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.
Got questions? Get instant answers now!
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
Got questions? Get instant answers now!
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.
Got questions? Get instant answers now!
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
Got questions? Get instant answers now!
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?
Got questions? Get instant answers now!
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
Got questions? Get instant answers now!
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?
Got questions? Get instant answers now!
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?
Got questions? Get instant answers now!
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?
Got questions? Get instant answers now!
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
Got questions? Get instant answers now!
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?
Got questions? Get instant answers now!
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?
Got questions? Get instant answers now!
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?
Got questions? Get instant answers now!
Questions & Answers
how does Neisseria cause meningitis
is the branch of biology that deals with the study of microorganisms.
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
How bacteria create energy to survive?
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
which site have a normal flora
Many sites of the body have it
Skin
Nasal cavity
Oral cavity
Gastro intestinal tract
Safaa
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Binomial nomenclature
adeolu
Got questions? Join the online conversation and get instant answers!
Source:
OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
Google Play and the Google Play logo are trademarks of Google Inc.