# 1.4 Homework: functions in the real world

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This module provides practice problems designed to mimic real life applications of functions.

Laura is selling doughnuts for 35¢ each. Each customer fills a box with however many doughnuts he wants, and then brings the box to Laura to pay for them. Let n represent the number of doughnuts in a box, and let $c$ represent the cost of the box (in cents).

• If the box has 3 doughnuts, how much does the box cost?
• If $c=\text{245}$ , how much does the box cost? How many doughnuts does it have?
• If a box has n doughnuts, how much does it cost?
• Write a function $c\left(n\right)$ that gives the cost of a box , as a function of the number of doughnuts in the box.

Worth is doing a scientific study of graffiti in the downstairs boy’s room. On the first day of school, there is no graffiti. On the second day, there are two drawings. On the third day, there are four drawings. He forgets to check on the fourth day, but on the fifth day, there are eight drawings. Let d represent the day, and g represent the number of graffiti marks that day.

• Fill in the following table, showing Worth’s four data points.  d (day) g (number of graffiti marks)
• If this pattern keeps up, how many graffiti marks will there be on day 10?
• If this pattern keeps up, on what day will there be 40 graffiti marks?
• Write a function $g\left(d\right)$ ) that gives the number of graffiti marks as a function of the day .

Each of the following is a set of points. Next to each one, write “yes” if that set of points could have been generated by a function, and “no” if it could not have been generated by a function. (You do not have to figure out what the function is. But you may want to try for fun—I didn’t just make up numbers randomly…)

• $\left(1,-1\right)\left(3,-3\right)\left(-1,-1\right)\left(-3,-3\right)$ ________
• $\left(1,\pi \right)\left(3,\pi \right)\left(9,\pi \right)\left(\pi ,\pi \right)$ ________
• $\left(1,1\right)\left(-1,1\right)\left(2,4\right)\left(-2,4\right)\left(3,9\right)\left(-3,9\right)$ ________
• $\left(1,1\right)\left(1,-1\right)\left(4,2\right)\left(4,-2\right)\left(9,3\right)\left(9,-3\right)$ ________
• $\left(1,1\right)\left(2,3\right)\left(3,6\right)\left(4,\text{10}\right)$ ________

$f\left(x\right)={x}^{2}+2x+1$

• $f\left(2\right)=$
• $f\left(-1\right)=$
• $f\left(\frac{3}{2}\right)=$
• $f\left(y\right)=$
• $f\left(\text{spaghetti}\right)=$
• $f\left(\sqrt{x}\right)$
• $f\left(f\left(x\right)\right)$

Make up a function that has something to do with movies .

• Think of a scenario where there are two numbers, one of which depends on the other. Describe the scenario, clearly identifying the independent variable and the dependent variable .
• Write the function that shows how the dependent variable depends on the independent variable.
• Now, plug in an example number to show how it works.

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
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Berger describes sociologists as concerned with
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