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Verbal

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.

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

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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.

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

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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.

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Numeric

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?

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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.

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

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Find the carrying capacity.

150

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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.

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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

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

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Technology

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

logarithmic

Graph of the question’s table.
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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
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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

logarithmic

Graph of the question’s table.
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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
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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 mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
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Practice Key Terms 6

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Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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