4.6 Exponential and logarithmic models  (Page 10/16)

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A wooden artifact from an archeological dig contains 60 percent of the carbon-14 that is present in living trees. To the nearest year, about how many years old is the artifact? (The half-life of carbon-14 is $\text{\hspace{0.17em}}\text{573}0\text{\hspace{0.17em}}$ years.)

A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was $\text{\hspace{0.17em}}1350\text{\hspace{0.17em}}$ bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after $\text{\hspace{0.17em}3\hspace{0.17em}}$ hours?

$f\left(t\right)=1350{e}^{\left(0.03466t\right)};\text{\hspace{0.17em}}$ after 3 hours: $\text{\hspace{0.17em}}P\left(180\right)\approx 691,200$

For the following exercises, use this scenario: A biologist recorded a count of $\text{\hspace{0.17em}}360\text{\hspace{0.17em}}$ bacteria present in a culture after $\text{\hspace{0.17em}}5\text{\hspace{0.17em}}$ minutes and $\text{\hspace{0.17em}}1000\text{\hspace{0.17em}}$ bacteria present after $\text{\hspace{0.17em}}20\text{\hspace{0.17em}}$ minutes.

To the nearest whole number, what was the initial population in the culture?

Rounding to six significant digits, write an exponential equation representing this situation. To the nearest minute, how long did it take the population to double?

$f\left(t\right)=256{e}^{\left(0.068110t\right)};\text{\hspace{0.17em}}$ doubling time: about $\text{\hspace{0.17em}}10\text{\hspace{0.17em}}$ minutes

For the following exercises, use this scenario: A pot of boiling soup with an internal temperature of $\text{\hspace{0.17em}}\text{100°}\text{\hspace{0.17em}}$ Fahrenheit was taken off the stove to cool in a room. After fifteen minutes, the internal temperature of the soup was

Use Newton’s Law of Cooling to write a formula that models this situation.

To the nearest minute, how long will it take the soup to cool to

about $\text{\hspace{0.17em}}\text{88}\text{\hspace{0.17em}}$ minutes

To the nearest degree, what will the temperature be after $\text{\hspace{0.17em}}2\text{\hspace{0.17em}}$ and a half hours?

For the following exercises, use this scenario: A turkey is taken out of the oven with an internal temperature of $\text{\hspace{0.17em}}\text{165°F}\text{\hspace{0.17em}}$ and is allowed to cool in a $\text{\hspace{0.17em}}\text{75°F}\text{\hspace{0.17em}}$ room. After half an hour, the internal temperature of the turkey is $\text{\hspace{0.17em}}\text{145°F}\text{.}$

Write a formula that models this situation.

$T\left(t\right)=90{e}^{\left(-0.008377t\right)}+75,$ where $\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ is in minutes.

To the nearest degree, what will the temperature be after 50 minutes?

To the nearest minute, how long will it take the turkey to cool to

about $\text{\hspace{0.17em}}\text{113}\text{\hspace{0.17em}}$ minutes

For the following exercises, find the value of the number shown on each logarithmic scale. Round all answers to the nearest thousandth.

$\mathrm{log}\left(x\right)=1.5;\text{\hspace{0.17em}}x\approx 31.623$

Plot each set of approximate values of intensity of sounds on a logarithmic scale: Whisper: Vacuum: $\text{\hspace{0.17em}}{10}^{-4}\frac{W}{{m}^{2}},$ Jet:

Recall the formula for calculating the magnitude of an earthquake, $\text{\hspace{0.17em}}M=\frac{2}{3}\mathrm{log}\left(\frac{S}{{S}_{0}}\right).\text{\hspace{0.17em}}$ One earthquake has magnitude $\text{\hspace{0.17em}}\text{3}.\text{9}\text{\hspace{0.17em}}$ on the MMS scale. If a second earthquake has $\text{\hspace{0.17em}}\text{75}0\text{\hspace{0.17em}}$ times as much energy as the first, find the magnitude of the second quake. Round to the nearest hundredth.

MMS magnitude: $\text{\hspace{0.17em}}5.82$

For the following exercises, use this scenario: The equation $\text{\hspace{0.17em}}N\left(t\right)=\frac{500}{1+49{e}^{-0.7t}}\text{\hspace{0.17em}}$ models the number of people in a town who have heard a rumor after t days.

How many people started the rumor?

To the nearest whole number, how many people will have heard the rumor after 3 days?

$N\left(3\right)\approx 71$

As $\text{\hspace{0.17em}}t\text{\hspace{0.17em}}$ increases without bound, what value does $\text{\hspace{0.17em}}N\left(t\right)\text{\hspace{0.17em}}$ approach? Interpret your answer.

For the following exercise, choose the correct answer choice.

A doctor and injects a patient with $\text{\hspace{0.17em}}13\text{\hspace{0.17em}}$ milligrams of radioactive dye that decays exponentially. After $\text{\hspace{0.17em}}12\text{\hspace{0.17em}}$ minutes, there are $\text{\hspace{0.17em}}4.75\text{\hspace{0.17em}}$ milligrams of dye remaining in the patient’s system. Which is an appropriate model for this situation?

1. $f\left(t\right)=13{\left(0.0805\right)}^{t}$
2. $f\left(t\right)=13{e}^{0.9195t}$
3. $f\left(t\right)=13{e}^{\left(-0.0839t\right)}$
4. $f\left(t\right)=\frac{4.75}{1+13{e}^{-0.83925t}}$

C

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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