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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 573 0 years.)

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

f ( t ) = 1350 e ( 0.03466 t ) ; after 3 hours: P ( 180 ) 691 , 200

For the following exercises, use this scenario: A biologist recorded a count of 360 bacteria present in a culture after 5 minutes and 1000 bacteria present after 20 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 ( t ) = 256 e ( 0.068110 t ) ; doubling time: about 10 minutes

For the following exercises, use this scenario: A pot of boiling soup with an internal temperature of 100° Fahrenheit was taken off the stove to cool in a 69° F room. After fifteen minutes, the internal temperature of the soup was 95° F .

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 80° F?

about 88 minutes

To the nearest degree, what will the temperature be after 2 and a half hours?

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

Write a formula that models this situation.

T ( t ) = 90 e ( 0.008377 t ) + 75 , where t 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 110° F?

about 113 minutes

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

Number line to show log(x) is between -1 and 0.
Number line to show log(x) is between 1 and 2.

log ( x ) = 1.5 ; x 31.623

Plot each set of approximate values of intensity of sounds on a logarithmic scale: Whisper: 10 10   W m 2 , Vacuum: 10 4 W m 2 , Jet: 10 2   W m 2

Recall the formula for calculating the magnitude of an earthquake, M = 2 3 log ( S S 0 ) . One earthquake has magnitude 3 . 9 on the MMS scale. If a second earthquake has 75 0 times as much energy as the first, find the magnitude of the second quake. Round to the nearest hundredth.

MMS magnitude: 5.82

For the following exercises, use this scenario: The equation N ( t ) = 500 1 + 49 e 0.7 t 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 ( 3 ) 71

As t increases without bound, what value does N ( t ) approach? Interpret your answer.

For the following exercise, choose the correct answer choice.

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

  1. f ( t ) = 13 ( 0.0805 ) t
  2. f ( t ) = 13 e 0.9195 t
  3. f ( t ) = 13 e ( 0.0839 t )
  4. f ( t ) = 4.75 1 + 13 e 0.83925 t


Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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.
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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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