Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Rate of Change Problems

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 Next →

Example Question #1 : Rate Of Change Problems

Find the average rate of change of the function y=2e^x over the interval from x=0 to x=2 .

Possible Answers:

e^2

e^2-1

1-e^2

e(e-1)

Correct answer:

e^2-1

Explanation:

The average rate of change will be found by $\frac{f(2)-f(0)}{2-0}$ .

Here, f(2)=2e^2 , and f(0)=2e^0=2(1)=2 .

Now, we have $\frac{2e^2-2}{2-0}=\frac{2e^2-2}{2}=e^2-1$ .

Report an Error

Example Question #2 : Rate Of Change Problems

Let a function be defined by f(x)=-ln(x+1) .

Find the average rate of change of the function over [0,4] .

Possible Answers:

$\frac{ln5}{4}$

$-ln\frac{5}{4}$

$ln\frac{-5}{4}$

$-\frac{ln5}{4}$

Correct answer:

$-\frac{ln5}{4}$

Explanation:

We use the average rate of change formula, which gives us $\frac{f(4)-f(0)}{4-0}$ .

Now f(4)=-ln(4+1)=-ln5 , and f(0)=-ln(0+1)=-ln1=0 .

Therefore, the answer becomes $\frac{-ln5-0}{4-0}=-\frac{ln5}{4}$ .

Report an Error

Example Question #3 : Rate Of Change Problems

Suppose we can model the profit, , in dollars from selling items with the equation P(x)=3x^2-4x+2 .

Find the average rate of change of the profit from x=1 to x=4 .

Possible Answers:

Correct answer:

Explanation:

We need to apply the formula for the average rate of change to our profit equation. Thus we find the average rate of change is $\frac{P(4)-P(1)}{4-1}$ .

Since P(4)=3(4)^2-4(4)+2=3(16)-16+2=48-16+2=34 , and P(1)=3(1)^2-4(1)+2=3(1)-4+2=3-4+2=1 , we find that the average rate of change is $\frac{34-1}{4-1}=\frac{33}{3}=11$ .

Report an Error

Example Question #1 : Rate Of Change Problems

Let the profit, , (in thousands of dollars) earned from producing items be found by P(x)=2x^2-6x+25 .

Find the average rate of change in profit when production increases from 4 items to 5 items.

Possible Answers:

$\frac{4}{3}$

Correct answer:

Explanation:

Since P(5)=2(5)^2-6(5)+25 , we see that this equals 2(25)-30+25=50-30+25=20+25=45 . Now let's examine P(4) . P(4)=2(4)^2-6(4)+25=2(16)-24+25 which simplifies to .

Therefore the average rate of change formula gives us $\frac{f(5)-f(4)}{5-4}=\frac{45-33}{5-4}=\frac{12}{1}=12$ .

Report an Error

Example Question #1 : Rate Of Change Problems

Suppose that a customer purchases dog treats based on the sale price , where D(p)=15-p^2+p , where $1\leq p\leq3$ .

Find the average rate of change in demand when the price increases from $2 per treat to $3 per treat.

Possible Answers:

Correct answer:

Explanation:

D(3)=15-9+3=6+3=9

D(2)=15-4+2=13

Thus the average rate of change formula yields $\frac{9-13}{3-2}=\frac{-4}{1}=-4$ .

This implies that the demand drops as the price increases.

Report an Error

Example Question #1 : Rate Of Change Problems

A college freshman invests $100 in a savings account that pays 5% interest compounded continuously. Thus, the amount saved after years can be calculated by $A(t)=100e^{0.05t}$ .

Find the average rate of change of the amount in the account between t=0 and t=3 , the year the student expects to graduate.

Possible Answers:

$\$38.73$

$-\$5.39$

$\$38.39$

$\$5.39$

Correct answer:

$\$5.39$

Explanation:

$A(3)=100e^{0.05*3}=100e^{0.15}\approx \$116.18$ .

$A(0)=100e^{0.05*0}=100e^{0}=\$100.00$ .

Hence, the average rate of change formula gives us $\frac{A(3)-A(0)}{3-0}=\frac{\$116.18-\$100.00}{3-0}=\frac{\$16.18}{3}\approx \$5.39$ .

Report an Error

Example Question #1 : Rate Of Change Problems

Find the average rate of change of $y=\sqrt{x-3}$ between x=4 and x=7 .

Possible Answers:

$\frac{1}{3}$

$-\frac{1}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

The solution will be found by the formula $\frac{f(7)-f(4)}{7-4}$ .

Here f(7) gives us $\sqrt{7-3}=\sqrt{4}=2$ , and $f(4)=\sqrt{4-3}=\sqrt{1}=1$ .

Thus, we find that the average rate of change is $\frac{2-1}{7-4}=\frac{1}{3}$ .

Report an Error

Example Question #2 : Rate Of Change Problems

Find the average rate of change of y=2x^2+3x over the interval from x=1 to x=3 .

Possible Answers:

Correct answer:

Explanation:

The average rate of change will be $\frac{f(3)-f(1)}{3-1}$ .

f(3)=2(3)^2+3(3)=2(9)+9=18+9=27 .

f(1)=2(1)^2+3(1)=2(1)+3=2+3=5 .

This gives us $\frac{27-5}{3-1}=\frac{22}{2}=11$ .

Report an Error

Example Question #1 : Rate Of Change Problems

Find the average rate of change of y=-x^2+3x-6 over the interval from x=-2 to x=0 .

Possible Answers:

Correct answer:

Explanation:

The average rate of change will be $\frac{f(0)-f(-2)}{0-(-2)}$ .

Now f(0)=-(0)^2+3(0)-6=-0+0-6=-6 .

We also know f(-2)=-(-2)^2+3(-2)-6=-4-6-6=-16 .

So we have $\frac{-6-(-16)}{0-(-2)}=\frac{-6+16}{0+2}=\frac{10}{2}=5$ .

Report an Error

Example Question #10 : Rate Of Change Problems

Why can we make an educated guess that the average rate of change of f(x)=x^2 , between x=-1 and x=1 would be ?

Possible Answers:

We know f(x) is symmetrical on that interval.

We know f(x) is a polynomial.

We know f(x) is vertical on that interval.

We know f(x) is odd on that interval.

We know f(x) is horizontal on that interval.

Correct answer:

We know f(x) is symmetrical on that interval.

Explanation:

Because f(x) is symmetrical over the y axis, it increases exactly as much as it decreases on the interval from to . Thus the average rate of change on that interval will be .

Report an Error

← Previous 1 2 Next →

View Pre-Calculus Tutors

Andrew
Certified Tutor

University of Wisconsin-Stevens Point, Bachelor of Science, Mathematics. University of Wisconsin-Oshkosh, Master of Science, ...

View Pre-Calculus Tutors

Judge
Certified Tutor

SUNY College at Brockport, Bachelor of Science, Mathematics.

View Pre-Calculus Tutors

Christopher
Certified Tutor

Macomb Community College, Associate in Science, Biological and Physical Sciences.

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SSAT Tutors in Denver, Math Tutors in Boston, Chemistry Tutors in Phoenix, Algebra Tutors in San Francisco-Bay Area, Math Tutors in Atlanta, French Tutors in New York City, Math Tutors in New York City, Spanish Tutors in Seattle, GRE Tutors in Boston, Statistics Tutors in Dallas Fort Worth

Popular Courses & Classes

ACT Courses & Classes in Atlanta, GRE Courses & Classes in Boston, GRE Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in San Diego, LSAT Courses & Classes in Boston, SSAT Courses & Classes in Phoenix, SAT Courses & Classes in New York City, ACT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Los Angeles, SAT Courses & Classes in Houston

Popular Test Prep

SAT Test Prep in Philadelphia, GRE Test Prep in San Francisco-Bay Area, GMAT Test Prep in Denver, GMAT Test Prep in Los Angeles, MCAT Test Prep in New York City, ACT Test Prep in San Francisco-Bay Area, MCAT Test Prep in San Francisco-Bay Area, SAT Test Prep in Boston, SAT Test Prep in New York City, ISEE Test Prep in Los Angeles

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

Precalculus : Rate of Change Problems

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Rate Of Change Problems

Example Question #2 : Rate Of Change Problems

Example Question #3 : Rate Of Change Problems

Example Question #1 : Rate Of Change Problems

Example Question #1 : Rate Of Change Problems

Example Question #1 : Rate Of Change Problems

Example Question #1 : Rate Of Change Problems

Example Question #2 : Rate Of Change Problems

Example Question #1 : Rate Of Change Problems

Example Question #10 : Rate Of Change Problems

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: