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
$P(x<\text{5730})$ .

Sketch the graph. Shade the area of interest.

Find the probability.
$P(x<\text{5730})$ =

$P(x<\text{5730})$ = 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.
$P(x>\text{10000})$ =

$P(x>\text{10000})$ = 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
$P(x<k)=0\text{.}\text{30}$ .

$k$ = 2947.73

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?

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

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?