<< Chapter < Page Chapter >> Page >

Algebraic

For the following exercises, identify whether the statement represents an exponential function. Explain.

The average annual population increase of a pack of wolves is 25.

Got questions? Get instant answers now!

A population of bacteria decreases by a factor of 1 8 every 24 hours.

exponential; the population decreases by a proportional rate. .

Got questions? Get instant answers now!

The value of a coin collection has increased by 3.25 % annually over the last 20 years.

Got questions? Get instant answers now!

For each training session, a personal trainer charges his clients $ 5 less than the previous training session.

not exponential; the charge decreases by a constant amount each visit, so the statement represents a linear function. .

Got questions? Get instant answers now!

The height of a projectile at time t is represented by the function h ( t ) = 4.9 t 2 + 18 t + 40.

Got questions? Get instant answers now!

For the following exercises, consider this scenario: For each year t , the population of a forest of trees is represented by the function A ( t ) = 115 ( 1.025 ) t . In a neighboring forest, the population of the same type of tree is represented by the function B ( t ) = 82 ( 1.029 ) t . (Round answers to the nearest whole number.)

Which forest’s population is growing at a faster rate?

The forest represented by the function B ( t ) = 82 ( 1.029 ) t .

Got questions? Get instant answers now!

Which forest had a greater number of trees initially? By how many?

Got questions? Get instant answers now!

Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 20 years? By how many?

After t = 20 years, forest A will have 43 more trees than forest B.

Got questions? Get instant answers now!

Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 100 years? By how many?

Got questions? Get instant answers now!

Discuss the above results from the previous four exercises. Assuming the population growth models continue to represent the growth of the forests, which forest will have the greater number of trees in the long run? Why? What are some factors that might influence the long-term validity of the exponential growth model?

Answers will vary. Sample response: For a number of years, the population of forest A will increasingly exceed forest B, but because forest B actually grows at a faster rate, the population will eventually become larger than forest A and will remain that way as long as the population growth models hold. Some factors that might influence the long-term validity of the exponential growth model are drought, an epidemic that culls the population, and other environmental and biological factors.

Got questions? Get instant answers now!

For the following exercises, determine whether the equation represents exponential growth, exponential decay, or neither. Explain.

y = 220 ( 1.06 ) x

exponential growth; The growth factor, 1.06 , is greater than 1.

Got questions? Get instant answers now!

y = 11 , 701 ( 0.97 ) t

exponential decay; The decay factor, 0.97 , is between 0 and 1.

Got questions? Get instant answers now!

For the following exercises, find the formula for an exponential function that passes through the two points given.

( 0 , 6 ) and ( 3 , 750 )

Got questions? Get instant answers now!

( 0 , 2000 ) and ( 2 , 20 )

f ( x ) = 2000 ( 0.1 ) x

Got questions? Get instant answers now!

( 1 , 3 2 ) and ( 3 , 24 )

Got questions? Get instant answers now!

( 2 , 6 ) and ( 3 , 1 )

f ( x ) = ( 1 6 ) 3 5 ( 1 6 ) x 5 2.93 ( 0.699 ) x

Got questions? Get instant answers now!

( 3 , 1 ) and ( 5 , 4 )

Got questions? Get instant answers now!

For the following exercises, determine whether the table could represent a function that is linear, exponential, or neither. If it appears to be exponential, find a function that passes through the points.

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
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
Practice Key Terms 4

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask