Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 1 : Rate

Study concepts, example questions & explanations for Calculus 1

Create An Account

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Constant Of Proportionality

The rate of growth of the robot army of Cloudweb is proportional to the population. The population increased by 89 percent between 2034 and 2037. What is the constant of proportionality for this terrifying army which threatens man's dominance?

Possible Answers:

-0.46

0.76

0.09

1.35

0.21

Correct answer:

0.21

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population increased by 89 percent between 2034 and 2037, we can solve for this constant of proportionality:

$(1+0.89)y_0=y_0e^{k(2037-2034)}$

$1.89=e^{3k}$

3k=ln(1.89)

$k=\frac{ln(1.89)}{3}=0.21$

Report an Error

Example Question #2701 : Functions

The rate of decrease of the number of concert attendees to former teen heartthrob Justice Beaver is proportional to the population. The population decreased by 34 percent between 2013 and 2015. What is the constant of proportionality?

Possible Answers:

-0.08

-0.40

-0.21

0.15

-1.11

Correct answer:

-0.21

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population decreased by 34 percent between 2013 and 2015, we can solve for this constant of proportionality:

$(1-0.34)y_0=y_0e^{k(2015-2013)}$

$0.66=e^{2k}$

2k=ln(0.66)

$k=\frac{ln(0.66)}{2}=-0.21$

Report an Error

Example Question #911 : Rate

The rate of growth of the Land of Battlecraft players is proportional to the population. The population increased by 72 percent between February and October of 2015. What is the constant of proportionality?

Possible Answers:

0.068

0.118

0.093

0.012

0.059

Correct answer:

0.068

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population increased by 72 percent between February and October, we can solve for this constant of proportionality. It'll help to represent the months by their number in the year:

$(1+0.72)y_0=y_0e^{k(10-2)}$

$1.72=e^{8k}$

8k=ln(1.72)

$k=\frac{ln(1.72)}{8}=0.068$

Report an Error

Example Question #11 : Exponential Growth Applications

The rate of decrease of the gluten-eating demographic of the US is proportional to the population. The population decreased by 8 percent between 2014 and 2015. What is the constant of proportionality?

Possible Answers:

-0.097

-0.083

-0.109

-0.194

-0.177

Correct answer:

-0.083

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population decreased by 8 percent between 2014 and 2015, we can solve for this constant of proportionality:

$(1-0.08)y_0=y_0e^{k(2015-2014)}$

$0.92=e^{k}$

k=ln(0.92)

k=-0.083

Report an Error

Example Question #13 : How To Find Constant Of Proportionality Of Rate

The rate of growth of the monster population of Quiet Hillock is proportional to the population. The population increased by 145 percent between January and August of 1999. What is the constant of proportionality?

Possible Answers:

0.128

0.094

0.021

0.053

0.077

Correct answer:

0.128

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population increased by 145 percent between January and August, we can solve for this constant of proportionality. It will be helpful to designate the months by their numbers:

$(1+1.45)y_0=y_0e^{k(8-1)}$

$2.45=e^{7k}$

7k=ln(2.45)

$k=\frac{ln(2.45)}{7}=0.128$

Report an Error

Example Question #11 : Constant Of Proportionality

The rate of growth of the velociraptor population at Mesozoic Terrace is proportional to the population. The population increased by 49 percent between 2010 and 2015. What is the constant of proportionality?

Possible Answers:

0.56

1.01

0.08

0.12

0.73

Correct answer:

0.08

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population increased by 49 percent between 2010 and 2015, we can solve for this constant of proportionality:

$(1+0.49)y_0=y_0e^{k(2015-2010)}$

$1.49=e^{5k}$

5k=ln(1.49)

$k=\frac{ln(1.49)}{5}=0.08$

Report an Error

Example Question #21 : Constant Of Proportionality

The rate of growth of the hogs in Houston is proportional to the population. The population increased from 500 to 900 between 2013 and 2015. What is the expected population in 2020?

Possible Answers:

5321

1920

3914

4196

1900

Correct answer:

3914

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population increased from 500 to 900 between 2013 and 2015, we can solve for this constant of proportionality:

$900=500e^{k(2015-2013)}$

$\frac{900}{500}=e^{2k}$

$2k=ln(\frac{900}{500})$

$k=\frac{ln(\frac{900}{500})}{2}=0.294$

Using this, we can calculate the expected value after five years from 2015:

$P=900e^{5(0.294)}\approx 3914$

Report an Error

Example Question #21 : How To Find Constant Of Proportionality Of Rate

The rate of growth of the population of mad donkeys is proportional to the population. The population increased from 1450 to 1965 between 2011 and 2015. What is the expected population in 2019?

Possible Answers:

3125

4009

2987

2480

2663

Correct answer:

2663

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population increased from 1450 to 1965 between 2011 and 2015, we can solve for this constant of proportionality:

$1965=1450e^{k(2015-2011)}$

$\frac{1965}{1450}=e^{4k}$

$4k=ln(\frac{1965}{1450})$

$k=\frac{ln(\frac{1965}{1450})}{4}=0.076$

Using this, we can calculate the expected value from 2015 to 2019:

$P=1965e^{4(0.076)} \approx 2663$

Report an Error

Example Question #21 : How To Find Constant Of Proportionality Of Rate

The rate of growth of the population of lice in a field is proportional to the population. The population increased from 10987 to 15612 between January and March. What is the expected population in October?

Possible Answers:

58799

41513

53519

67183

49857

Correct answer:

53519

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population increased from 10987 to 15612 between January and March, we can solve for this constant of proportionality. Represent the months as their number in the calendar:

$15612=10987e^{k(3-1)}$

$\frac{15612}{10987}=e^{2k}$

$2k=ln(\frac{15612}{10987})$

$k=\frac{ln(\frac{15612}{10987})}{2}=0.176$

Using this, we can calculate the expected value from March to October:

$P=15612e^{(10-3)(0.176)} \approx 53519$

Report an Error

Example Question #24 : How To Find Constant Of Proportionality Of Rate

The rate of growth of the population of fruit flies in a salad bar is proportional to the population. The population increased from 38 to 92 in the course of 60 minutes. What is the expected population after another 60 minutes?

Possible Answers:

272

195

146

222

173

Correct answer:

222

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population increased from 38 to 92 in the course of 60 minutes, we can solve for this constant of proportionality:

$92=38e^{k(60)}$

$\frac{92}{38}=e^{60k}$

$60k=ln(\frac{92}{38})$

$k=\frac{ln(\frac{92}{38})}{60}=0.0147$

Using this, we can calculate the expected value after another 60 minutes:

$P=92e^{60(0.0147)} \approx 222$

Report an Error

View Calculus Tutors

Monica
Certified Tutor

Purdue University-Main Campus, Bachelor of Science, Mathematics Teacher Education. Concordia University-Ann Arbor, Master of ...

View Calculus Tutors

Robert
Certified Tutor

Daytona State College, Bachelor in Arts, Teaching English as a Second Language (ESL).

View Calculus Tutors

Muhammad
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Neuroscience.

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GMAT Tutors in Dallas Fort Worth, GRE Tutors in Denver, LSAT Tutors in Philadelphia, Reading Tutors in Seattle, Computer Science Tutors in Seattle, LSAT Tutors in Denver, ACT Tutors in Washington DC, Statistics Tutors in Dallas Fort Worth, Calculus Tutors in Philadelphia, SAT Tutors in Phoenix

Popular Courses & Classes

GMAT Courses & Classes in Chicago, Spanish Courses & Classes in Chicago, SSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in San Diego, SAT Courses & Classes in San Diego, ISEE Courses & Classes in Los Angeles, LSAT Courses & Classes in Philadelphia, LSAT Courses & Classes in Phoenix, GMAT Courses & Classes in Dallas Fort Worth, Spanish Courses & Classes in New York City

Popular Test Prep

ISEE Test Prep in Philadelphia, LSAT Test Prep in Los Angeles, GMAT Test Prep in Miami, GMAT Test Prep in New York City, SSAT Test Prep in Dallas Fort Worth, MCAT Test Prep in San Francisco-Bay Area, GMAT Test Prep in Atlanta, SSAT Test Prep in New York City, SSAT Test Prep in Philadelphia, GMAT Test Prep in Houston

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Calculus 1 : Rate

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #11 : Constant Of Proportionality

Example Question #2701 : Functions

Example Question #911 : Rate

Example Question #11 : Exponential Growth Applications

Example Question #13 : How To Find Constant Of Proportionality Of Rate

Example Question #11 : Constant Of Proportionality

Example Question #21 : Constant Of Proportionality

Example Question #21 : How To Find Constant Of Proportionality Of Rate

Example Question #21 : How To Find Constant Of Proportionality Of Rate

Example Question #24 : How To Find Constant Of Proportionality Of Rate

All Calculus 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: