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Section exercises


With what kind of exponential model would half-life be associated? What role does half-life play in these models?

Half-life is a measure of decay and is thus associated with exponential decay models. The half-life of a substance or quantity is the amount of time it takes for half of the initial amount of that substance or quantity to decay.

What is carbon dating? Why does it work? Give an example in which carbon dating would be useful.

With what kind of exponential model would doubling time be associated? What role does doubling time play in these models?

Doubling time is a measure of growth and is thus associated with exponential growth models. The doubling time of a substance or quantity is the amount of time it takes for the initial amount of that substance or quantity to double in size.

Define Newton’s Law of Cooling. Then name at least three real-world situations where Newton’s Law of Cooling would be applied.

What is an order of magnitude? Why are orders of magnitude useful? Give an example to explain.

An order of magnitude is the nearest power of ten by which a quantity exponentially grows. It is also an approximate position on a logarithmic scale; Sample response: Orders of magnitude are useful when making comparisons between numbers that differ by a great amount. For example, the mass of Saturn is 95 times greater than the mass of Earth. This is the same as saying that the mass of Saturn is about 10 2 times, or 2 orders of magnitude greater, than the mass of Earth.


The temperature of an object in degrees Fahrenheit after t minutes is represented by the equation T ( t ) = 68 e 0.0174 t + 72. To the nearest degree, what is the temperature of the object after one and a half hours?

For the following exercises, use the logistic growth model f ( x ) = 150 1 + 8 e 2 x .

Find and interpret f ( 0 ) . Round to the nearest tenth.

f ( 0 ) 16.7 ; The amount initially present is about 16.7 units.

Find and interpret f ( 4 ) . Round to the nearest tenth.

Find the carrying capacity.


Graph the model.

Determine whether the data from the table could best be represented as a function that is linear, exponential, or logarithmic. Then write a formula for a model that represents the data.

x f ( x )
–2 0.694
–1 0.833
0 1
1 1.2
2 1.44
3 1.728
4 2.074
5 2.488

exponential; f ( x ) = 1.2 x

Rewrite f ( x ) = 1.68 ( 0.65 ) x as an exponential equation with base e to five significant digits.


For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic.

x f ( x )
1 2
2 4.079
3 5.296
4 6.159
5 6.828
6 7.375
7 7.838
8 8.238
9 8.592
10 8.908


Graph of the question’s table.
x f ( x )
1 2.4
2 2.88
3 3.456
4 4.147
5 4.977
6 5.972
7 7.166
8 8.6
9 10.32
10 12.383
x f ( x )
4 9.429
5 9.972
6 10.415
7 10.79
8 11.115
9 11.401
10 11.657
11 11.889
12 12.101
13 12.295


Graph of the question’s table.
x f ( x )
1.25 5.75
2.25 8.75
3.56 12.68
4.2 14.6
5.65 18.95
6.75 22.25
7.25 23.75
8.6 27.8
9.25 29.75
10.5 33.5

For the following exercises, use a graphing calculator and this scenario: the population of a fish farm in t years is modeled by the equation P ( t ) = 1000 1 + 9 e 0.6 t .

Questions & Answers

what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Essential precalculus, part 1. OpenStax CNX. Aug 26, 2015 Download for free at http://legacy.cnx.org/content/col11871/1.1
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