# 4.2 Modeling with linear functions  (Page 7/9)

 Page 7 / 9

If the function $\text{\hspace{0.17em}}P\text{\hspace{0.17em}}$ is graphed, find and interpret the slope of the function.

When will the population reach 100,000?

Ten years after the model began

What is the population in the year 12 years from the onset of the model?

For the following exercises, consider this scenario: The weight of a newborn is 7.5 pounds. The baby gained one-half pound a month for its first year.

Find the linear function that models the baby’s weight $\text{\hspace{0.17em}}W\text{\hspace{0.17em}}$ as a function of the age of the baby, in months, $\text{\hspace{0.17em}}t.$

$W\left(t\right)=0.5t+7.5$

Find a reasonable domain and range for the function $\text{\hspace{0.17em}}W.$

If the function $\text{\hspace{0.17em}}W\text{\hspace{0.17em}}$ is graphed, find and interpret the x - and y -intercepts.

$\left(-15,\text{}0\right)\text{\hspace{0.17em}}$ : The x -intercept is not a plausible set of data for this model because it means the baby weighed 0 pounds 15 months prior to birth. $\text{\hspace{0.17em}}\left(0,\text{7}.\text{5}\right)\text{\hspace{0.17em}}$ : The baby weighed 7.5 pounds at birth.

If the function W is graphed, find and interpret the slope of the function.

When did the baby weight 10.4 pounds?

At age 5.8 months

What is the output when the input is 6.2?

For the following exercises, consider this scenario: The number of people afflicted with the common cold in the winter months steadily decreased by 205 each year from 2005 until 2010. In 2005, 12,025 people were inflicted.

Find the linear function that models the number of people inflicted with the common cold $\text{\hspace{0.17em}}C\text{\hspace{0.17em}}$ as a function of the year, $\text{\hspace{0.17em}}t.$

$C\left(t\right)=12,025-205t$

Find a reasonable domain and range for the function $\text{\hspace{0.17em}}C.$

If the function $\text{\hspace{0.17em}}C\text{\hspace{0.17em}}$ is graphed, find and interpret the x - and y -intercepts.

$\left(\text{58}.\text{7},\text{}0\right):\text{\hspace{0.17em}}$ In roughly 59 years, the number of people inflicted with the common cold would be 0. $\text{\hspace{0.17em}}\left(0,\text{12},0\text{25}\right)\text{\hspace{0.17em}}$ Initially there were 12,025 people afflicted by the common cold.

If the function $\text{\hspace{0.17em}}C\text{\hspace{0.17em}}$ is graphed, find and interpret the slope of the function.

When will the output reach 0?

2063

In what year will the number of people be 9,700?

## Graphical

For the following exercises, use the graph in [link] , which shows the profit, $\text{\hspace{0.17em}}y,$ in thousands of dollars, of a company in a given year, $\text{\hspace{0.17em}}t,$ where $\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ represents the number of years since 1980.

Find the linear function $\text{\hspace{0.17em}}y,$ where $\text{\hspace{0.17em}}y\text{\hspace{0.17em}}$ depends on $\text{\hspace{0.17em}}t,$ the number of years since 1980.

$y=-2t\text{+180}$

Find and interpret the y -intercept.

Find and interpret the x -intercept.

In 2070, the company’s profit will be zero.

Find and interpret the slope.

For the following exercises, use the graph in [link] , which shows the profit, $\text{\hspace{0.17em}}y,$ in thousands of dollars, of a company in a given year, $\text{\hspace{0.17em}}t,$ where $\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ represents the number of years since 1980.

Find the linear function $\text{\hspace{0.17em}}y,$ where $\text{\hspace{0.17em}}y\text{\hspace{0.17em}}$ depends on $\text{\hspace{0.17em}}t,$ the number of years since 1980.

$y=\text{3}0t-\text{3}00$

Find and interpret the y -intercept.

$\left(0,-300\right);$ In 1980, the company lost $300,000. Find and interpret the x -intercept. Find and interpret the slope. $y=30t-300\text{\hspace{0.17em}}$ of form $\text{\hspace{0.17em}}y=mx+b,\text{m}=30.$ For each year after 1980, the company's profits increased$30,000 per year

## Numeric

For the following exercises, use the median home values in Mississippi and Hawaii (adjusted for inflation) shown in [link] . Assume that the house values are changing linearly.

Year Mississippi Hawaii
1950 $25,200$74,400
2000 $71,400$272,700

In which state have home values increased at a higher rate?

#### Questions & Answers

A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=250,000csc(π30x). Graph g(x) on the interval [0, 35]. Evaluate g(5)  and interpret the information. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? Find and discuss the meaning of any vertical asymptotes.
Kaitlyn Reply
The sequence is {1,-1,1-1.....} has
amit Reply
circular region of radious
Kainat Reply
how can we solve this problem
Joel Reply
Sin(A+B) = sinBcosA+cosBsinA
Eseka Reply
Prove it
Eseka
Please prove it
Eseka
hi
Joel
June needs 45 gallons of punch. 2 different coolers. Bigger cooler is 5 times as large as smaller cooler. How many gallons in each cooler?
Arleathia Reply
7.5 and 37.5
Nando
find the sum of 28th term of the AP 3+10+17+---------
Prince Reply
I think you should say "28 terms" instead of "28th term"
Vedant
the 28th term is 175
Nando
192
Kenneth
if sequence sn is a such that sn>0 for all n and lim sn=0than prove that lim (s1 s2............ sn) ke hole power n =n
SANDESH Reply
write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
give me the waec 2019 questions
Aaron Reply

### Read also:

#### Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

 By By