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 #3771 : Calculus

The rate of decrease of the bacteria in the presence of a UV sterilization lamp is proportional to the population. The population on a surgical instrument decreases from 2900 to 500 in the course of an hour. How many more minutes will it take to bring the count under 25?

Possible Answers:

265

103

134

Correct answer:

103

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, represents a measure of elapsed time relative to this population value, and is the constant of proportionality.

Since the population decreases from 2900 to 500 in the course of an hour (or 60 minutes), we can solve for this constant of proportionality:

$500=2900e^{60k}$

$\frac{5}{29}=e^{60k}$

$60k=ln(\frac{5}{29})$

$k=\frac{ln(\frac{5}{29})}{60}=-0.0293$

Now that the constant of proportionality is known, we can use it to estimate our time point:

$25=500e^{-0.0293t}$

$-0.0293t=ln(\frac{1}{20})$

$t=\frac{ln(\frac{1}{20})}{-0.0293}=102.2 \rightarrow103$

Report an Error

Example Question #3771 : Calculus

The rate of change of the yeast in a lump of unbaked sour dough is proportional to the population. The population increased by 5 percent over the course of 15 minutes. What is the constant of proportionality in minutes^-1?

Possible Answers:

0.0111

0.0033

0.0004

0.0756

0.0283

Correct answer:

0.0033

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 5 percent over the course of 15 minutes, we can solve for this constant of proportionality:

$(1+0.05)y_0=y_0e^{15k}$

$1.05=e^{15k}$

15k=ln(1.05)

$k=\frac{ln(1.05)}{15}=0.0033$

Report an Error

Example Question #953 : Rate

The rate of change of the culture size of baceteria on a dirty plate is proportional to the population. The population increased by 32 percent over the course of 35 minutes. What is the constant of proportionality in minutes^-1?

Possible Answers:

0.0183

0.0079

0.0203

0.0018

0.099

Correct answer:

0.0079

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 32 percent over the course of 35 minutes, we can solve for this constant of proportionality:

$(1+0.32)y_0=y_0e^{35k}$

$1.32=e^{35k}$

35k=ln(1.32)

$k=\frac{ln(1.32)}{35}=0.0079$

Report an Error

Example Question #954 : Rate

The rate of change of the population of Crystal Cove salmon is proportional to the population. The population increased by 23 percent over the course of two years. What is the constant of proportionality in years^-1?

Possible Answers:

0.122

0.233

0.157

0.104

0.188

Correct answer:

0.104

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 23 percent over the course of two years, we can solve for this constant of proportionality:

$(1+0.23)y_0=y_0e^{2k}$

$1.23=e^{2k}$

2k=ln(1.23)

$k=\frac{ln(1.23)}{2}=0.104$

Report an Error

Example Question #955 : Rate

The rate of change of the Bjorg is proportional to the population. The population increased by 189 percent over the course of 1 year. What is the constant of proportionality in years^-1?

Possible Answers:

0.166

0.753

0.424

1.061

0.899

Correct answer:

1.061

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 189 percent over the course of 1 year, we can solve for this constant of proportionality:

$(1+1.89)y_0=y_0e^{k(1)}$

$2.89=e^{k}$

k=ln(2.89)=1.061

Report an Error

Example Question #3771 : Calculus

The rate of change of the E. coli number on a piece of raw meat is proportional to the population. The population increased by 6300 percent over the course of 2 hours. What is the constant of proportionality in minutes^-1?

Possible Answers:

0.152

0.989

1.388

2.079

0.035

Correct answer:

0.035

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 , we can solve for this constant of proportionality. Remember what units the problem asks for:

$(1+63)y_0=y_0e^{k(2*60)}$

$64=e^{120k}$

120k=ln(64)

$k=\frac{ln(64)}{120}$

Report an Error

Example Question #61 : How To Find Constant Of Proportionality Of Rate

The rate of change of the staph bacterial number in a petri dish is proportional to the population. The population increased by 300 percent over the course of 40 minutes. What is the constant of proportionality in hours^-1?

Possible Answers:

0.007

8.225

2.079

0.034

0.582

Correct answer:

2.079

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 300 percent over the course of 40 minutes, we can solve for this constant of proportionality. Mind the units required:

$(1+3)y_0=y_0e^{k(\frac{40}{60})}$

$4=e^{\frac{2}{3}k}$

$\frac{2}{3}k=ln(4)$

$k=\frac{ln(4)}{\frac{2}{3}}=2.079$

Report an Error

Example Question #61 : How To Find Constant Of Proportionality Of Rate

The rate of change of the salmonella prescence in a contaminated egg is proportional to the population. The population increased by 0.33 percent over the course of 89 seconds. What is the constant of proportionality in hours^-1?

Possible Answers:

0.00003

0.02824

0.00522

0.13326

4.83107

Correct answer:

0.13326

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 0.33 percent over the course of 89 seconds, we can solve for this constant of proportionality. Mind the unites:

$(1+0.0033)y_0=y_0e^{k(\frac{89}{3600})}$

$1.0033=e^{\frac{89}{3600}k}$

$\frac{89}{3600}k=ln(1.0033)$

$k=\frac{ln(1.0033)}{\frac{89}{3600}}=0.1333$

Report an Error

Example Question #61 : Constant Of Proportionality

The rate of change of the number of black bears in an untouched stretch of California forest is proportional to the population. The population increased by 57 percent between January of 2013 and January of 2015. What is the constant of proportionality in months^-1?

Possible Answers:

10.826

5.233

0.628

0.019

0.451

Correct answer:

0.019

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 57 percent between January of 2013 and January of 2015, we can solve for this constant of proportionality. Be careful of the units used, however:

$(1+0.57)y_0=y_0e^{k(12(2015-2013))}$

$1.57=e^{24k}$

24k=ln(1.57)

$k=\frac{ln(1.57)}{24}=0.019$

Report an Error

Example Question #960 : Rate

The rate of change of the number cholera causing bacteria in a stagnant pool is proportional to the population. The population increased by 83 percent between 3:15 and 4:30. What is the constant of proportionality in hours^-1?

Possible Answers:

8.113

0.029

0.483

0.405

0.008

Correct answer:

0.483

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 83 percent between 3:15 and 4:30, we can solve for this constant of proportionality. Since we're asked for the units of inverse hours, convert the minutes to decimals by dividing by 60:

$(1+0.83)y_0=y_0e^{k(4.5-3.25)}$

$1.83=e^{1.25k}$

1.25k=ln(1.83)

$k=\frac{ln(1.83)}{1.25}=0.483$

Report an Error

View Calculus Tutors

James
Certified Tutor

Purdue University-Main Campus, Doctor of Education, Mathematics Teacher Education.

View Calculus Tutors

Ryanto
Certified Tutor

Excelsior College, Albany NY, Bachelor, Business with Math Minor. University of Houston, Master's/Graduate, Accounting.

View Calculus Tutors

Nikhil
Certified Tutor

University of Kansas, Master of Science, Mechanical Engineering.

All Calculus 1 Resources

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

Popular Subjects

Chemistry Tutors in Denver, GMAT Tutors in Philadelphia, French Tutors in San Diego, English Tutors in San Diego, SAT Tutors in New York City, Biology Tutors in Chicago, French Tutors in New York City, Math Tutors in San Diego, Computer Science Tutors in Seattle, Spanish Tutors in Miami

Popular Courses & Classes

GMAT Courses & Classes in Miami, LSAT Courses & Classes in New York City, ISEE Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Boston, GRE Courses & Classes in Washington DC, LSAT Courses & Classes in Houston, MCAT Courses & Classes in Seattle, Spanish Courses & Classes in Chicago, LSAT Courses & Classes in Phoenix, Spanish Courses & Classes in Philadelphia

Popular Test Prep

ISEE Test Prep in Dallas Fort Worth, ACT Test Prep in Los Angeles, ISEE Test Prep in Atlanta, GMAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Phoenix, ISEE Test Prep in Houston, MCAT Test Prep in Los Angeles, SSAT Test Prep in Boston, MCAT Test Prep in Boston, GRE Test Prep in Denver

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 #3771 : Calculus

Example Question #3771 : Calculus

Example Question #953 : Rate

Example Question #954 : Rate

Example Question #955 : Rate

Example Question #3771 : Calculus

Example Question #61 : How To Find Constant Of Proportionality Of Rate

Example Question #61 : How To Find Constant Of Proportionality Of Rate

Example Question #61 : Constant Of Proportionality

Example Question #960 : Rate

All Calculus 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: