# 6.6 Practice 2: exponential distribution

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In this module the student will explore the properties of data with an exponential distribution.

## Student learning outcomes

• The student will analyze data following the exponential distribution.

## Given

Carbon-14 is a radioactive element with a half-life of about 5730 years. Carbon-14 is said to decay exponentially. The decay rate is 0.000121 . We start with 1 gram of carbon-14. We are interested in the time (years) it takes to decay carbon-14.

## Describe the data

What is being measured here?

Are the data discrete or continuous?

Continuous

In words, define the Random Variable $X$ .

$X$ = Time (years) to decay carbon-14

What is the decay rate ( $m$ )?

$m$ = 0.000121

The distribution for $X$ is:

$X$ ~ Exp(0.000121)

## Probability

Find the amount (percent of 1 gram) of carbon-14 lasting less than 5730 years. This means, find $P\left(x<\text{5730}\right)$ .

• Sketch the graph. Shade the area of interest.
• Find the probability. $P\left(x<\text{5730}\right)$ =
• $P\left(x<\text{5730}\right)$ = 0.5001

Find the percentage of carbon-14 lasting longer than 10,000 years.

• Sketch the graph. Shade the area of interest.
• Find the probability. $P\left(x>\text{10000}\right)$ =
• $P\left(x>\text{10000}\right)$ = 0.2982

Thirty percent (30%) of carbon-14 will decay within how many years?

• Sketch the graph. Shade the area of interest.
• Find the value $k$ such that $P\left(x .
• $k$ = 2947.73

#### Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
how did you get the value of 2000N.What calculations are needed to arrive at it
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