We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Common Core: High School - Functions : Growth and Decay by Contant Percent Rate: CCSS.Math.Content.HSF-LE.A.1c

Study concepts, example questions & explanations for Common Core: High School - Functions

Create An Account

All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #21 : Linear, Quadratic, & Exponential Models*

An anti-diabetic drug, has a half-life of about hours. If a patient was administered $200 mg of the drug at $8:00 am , how much is left at $1:00 pm ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Possible Answers:

$A=90\textup{ mg}$

$A=94\textup{ mg}$

$A=184\textup{ mg}$

$A=84\textup{ mg}$

$A=82\textup{ mg}$

Correct answer:

$A=84\textup{ mg}$

Explanation:

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

For the purpose of Common Core Standards, recognize situations that have a exponential growth or decay over a certain interval, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\\A_0=\textup{Intial Amount}=200\textup{ mg} \\h=\textup{half life}=4\textup{ hours} \\t_f=1:00\textup{ pm} \\t_i=8:00\textup{ am} \\A=?$

Step 2: Calculate .

$1:00-8:00\rightarrow 5 \textup{ hours }$

Step 3: Substitute in known values into the half life formula to solve for .

$A=200\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{5}{4}}$

$A=200\textup{ mg}\cdot \left(\frac{1}{2}\right)^{1.25}$

$A=200\textup{ mg}\cdot 0.420$

$A=84\textup{ mg}$

Report an Error

Example Question #22 : Linear, Quadratic, & Exponential Models*

An anti-diabetic drug, has a half-life of about 6.2 hours. If a patient was administered $500 mg of the drug at $8:21 am , how much is left at $4:34 pm ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Possible Answers:

$A=199.57\textup{ mg}$

$A=199.99\textup{ mg}$

$A=159.57\textup{ mg}$

$A=197.57\textup{ mg}$

$A=128.57\textup{ mg}$

Correct answer:

$A=199.57\textup{ mg}$

Explanation:

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\\A_0=\textup{Intial Amount}=500\textup{ mg} \\h=\textup{half life}=6.2\textup{ hours} \\t_f=4:34\textup{pm} \\t_i=8:21\textup{ am} \\A=?$

Step 2: Calculate .

$4:34-8:21\rightarrow 8 \textup{ hours }13\textup{ minutes}$

Recall that there are sixty minutes in an hour therefore,

$8\textup{ hours }13\textup{ minutes}=8+\frac{13}{60}=8.216\overline{6}$

Step 3: Substitute in known values into the half life formula to solve for .

$A=500\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{8.216\overline{6}}{6.2}}$

$A=500\textup{ mg}\cdot \left(\frac{1}{2}\right)^{1.325}$

$A=500\textup{ mg}\cdot 0.399$

$A=199.57\textup{ mg}$

Report an Error

Example Question #23 : Linear, Quadratic, & Exponential Models*

An particular medicine, has a half-life of about hours. If a patient was administered $50 mg of the drug at $11 am , how much is left at $2 pm ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Possible Answers:

$A=15\textup{ mg}$

$A=45\textup{ mg}$

$A=20\textup{ mg}$

$A=30\textup{ mg}$

$A=25\textup{ mg}$

Correct answer:

$A=25\textup{ mg}$

Explanation:

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\\A_0=\textup{Intial Amount}=50\textup{ mg} \\h=\textup{half life}=3\textup{ hours} \\t_f=2:00\textup{ pm} \\t_i=11:00\textup{ am} \\A=?$

Step 2: Calculate .

$2:00-11:00\rightarrow 3 \textup{ hours }$

Step 3: Substitute in known values into the half life formula to solve for .

$A=50\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{3}{3}}$

$A=50\textup{ mg}\cdot \left(\frac{1}{2}\right)^{1}$

$A=50\textup{ mg}\cdot 0.50$

$A=25\textup{ mg}$

Report an Error

Example Question #24 : Linear, Quadratic, & Exponential Models*

An particular medicine, has a half-life of about hours. If a patient was administered $600 mg of the drug at $8:00 am , how much is left at $1:00 pm ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Possible Answers:

$A=360\textup{ mg}$

$A=466\textup{ mg}$

$A=266\textup{ mg}$

$A=306\textup{ mg}$

$A=366\textup{ mg}$

Correct answer:

$A=366\textup{ mg}$

Explanation:

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\\A_0=\textup{Intial Amount}=600\textup{ mg} \\h=\textup{half life}=7\textup{ hours} \\t_f=1:00\textup{ pm} \\t_i=8:00\textup{ am} \\A=?$

Step 2: Calculate .

$1:00-8:00\rightarrow 5 \textup{ hours }$

Step 3: Substitute in known values into the half life formula to solve for .

$A=600\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{5}{7}}$

$A=600\textup{ mg}\cdot \left(\frac{1}{2}\right)^{0.714}$

$A=600\textup{ mg}\cdot 0.61$

$A=366\textup{ mg}$

Report an Error

Example Question #25 : Linear, Quadratic, & Exponential Models*

An particular medicine, has a half-life of about hours. If a patient was administered $350 mg of the drug at $8:00 am , how much is left at $1:00 pm ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Possible Answers:

$A=195.65\textup{ mg}$

$A=169.35\textup{ mg}$

$A=198.75\textup{ mg}$

$A=196.35\textup{ mg}$

$A=197.35\textup{ mg}$

Correct answer:

$A=196.35\textup{ mg}$

Explanation:

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\\A_0=\textup{Intial Amount}=350\textup{ mg} \\h=\textup{half life}=6\textup{ hours} \\t_f=1:00\textup{ pm} \\t_i=8:00\textup{ am} \\A=?$

Step 2: Calculate .

$1:00-8:00\rightarrow 5 \textup{ hours }$

Step 3: Substitute in known values into the half life formula to solve for .

$A=350\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{5}{6}}$

$A=350\textup{ mg}\cdot \left(\frac{1}{2}\right)^{0.833}$

$A=350\textup{ mg}\cdot 0.561$

$A=196.35\textup{ mg}$

Report an Error

Example Question #26 : Linear, Quadratic, & Exponential Models*

An anti-diabetic drug, has a half-life of about 6.2 hours. If a patient was administered $800 mg of the drug at $8:21 am , how much is left at $4:34 pm ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Possible Answers:

$A=319.2\textup{ mg}$

$A=317.3\textup{ mg}$

$A=318.2\textup{ mg}$

$A=321.2\textup{ mg}$

$A=320.2\textup{ mg}$

Correct answer:

$A=319.2\textup{ mg}$

Explanation:

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\\A_0=\textup{Intial Amount}=800\textup{ mg} \\h=\textup{half life}=6.2\textup{ hours} \\t_f=4:34\textup{pm} \\t_i=8:21\textup{ am} \\A=?$

Step 2: Calculate .

$4:34-8:21\rightarrow 8 \textup{ hours }13\textup{ minutes}$

Recall that there are sixty minutes in an hour therefore,

$8\textup{ hours }13\textup{ minutes}=8+\frac{13}{60}=8.216\overline{6}$

Step 3: Substitute in known values into the half life formula to solve for .

$A=800\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{8.216\overline{6}}{6.2}}$

$A=800\textup{ mg}\cdot \left(\frac{1}{2}\right)^{1.325}$

$A=800\textup{ mg}\cdot 0.399$

$A=319.2\textup{ mg}$

Report an Error

Example Question #1 : Growth And Decay By Contant Percent Rate: Ccss.Math.Content.Hsf Le.A.1c

An anti-diabetic drug, has a half-life of about 6.2 hours. If a patient was administered $50 mg of the drug at $8:21 am , how much is left at $4:34 pm ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Possible Answers:

$A=21.95\textup{ mg}$

$A=18.95\textup{ mg}$

$A=17.95\textup{ mg}$

$A=19.95\textup{ mg}$

$A=19.97\textup{ mg}$

Correct answer:

$A=19.95\textup{ mg}$

Explanation:

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\\A_0=\textup{Intial Amount}=50\textup{ mg} \\h=\textup{half life}=6.2\textup{ hours} \\t_f=4:34\textup{pm} \\t_i=8:21\textup{ am} \\A=?$

Step 2: Calculate .

$4:34-8:21\rightarrow 8 \textup{ hours }13\textup{ minutes}$

Recall that there are sixty minutes in an hour therefore,

$8\textup{ hours }13\textup{ minutes}=8+\frac{13}{60}=8.216\overline{6}$

Step 3: Substitute in known values into the half life formula to solve for .

$A=50\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{8.216\overline{6}}{6.2}}$

$A=50\textup{ mg}\cdot \left(\frac{1}{2}\right)^{1.325}$

$A=50\textup{ mg}\cdot 0.399$

$A=19.95\textup{ mg}$

Report an Error

Example Question #2 : Growth And Decay By Contant Percent Rate: Ccss.Math.Content.Hsf Le.A.1c

An medicine, has a half-life of about 4.2 hours. If a patient was administered $100 mg of the drug at $8:21 am , how much is left at $4:34 pm ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Possible Answers:

$A=24.57\textup{ mg}$

$A=25.77\textup{ mg}$

$A=27.77\textup{ mg}$

$A=35.77\textup{ mg}$

$A=25.57\textup{ mg}$

Correct answer:

$A=25.77\textup{ mg}$

Explanation:

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\\A_0=\textup{Intial Amount}=100\textup{ mg} \\h=\textup{half life}=4.2\textup{ hours} \\t_f=4:34\textup{pm} \\t_i=8:21\textup{ am} \\A=?$

Step 2: Calculate .

$4:34-8:21\rightarrow 8 \textup{ hours }13\textup{ minutes}$

Recall that there are sixty minutes in an hour therefore,

$8\textup{ hours }13\textup{ minutes}=8+\frac{13}{60}=8.216\overline{6}$

Step 3: Substitute in known values into the half life formula to solve for .

$A=100\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{8.216\overline{6}}{4.2}}$

$A=100\textup{ mg}\cdot \left(\frac{1}{2}\right)^{1.9563}$

$A=100\textup{ mg}\cdot 0.2577$

$A=25.77\textup{ mg}$

Report an Error

Example Question #3 : Growth And Decay By Contant Percent Rate: Ccss.Math.Content.Hsf Le.A.1c

An certain medicine, has a half-life of about 3.4 hours. If a patient was administered $150 mg of the drug at $8:21 am , how much is left at $4:34 pm ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Possible Answers:

$A=28.09\textup{ mg}$

$A=28.39\textup{ mg}$

$A=29.09\textup{ mg}$

$A=28.08\textup{ mg}$

$A=29.08\textup{ mg}$

Correct answer:

$A=28.09\textup{ mg}$

Explanation:

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\\A_0=\textup{Intial Amount}=150\textup{ mg} \\h=\textup{half life}=3.4\textup{ hours} \\t_f=4:34\textup{pm} \\t_i=8:21\textup{ am} \\A=?$

Step 2: Calculate .

$4:34-8:21\rightarrow 8 \textup{ hours }13\textup{ minutes}$

Recall that there are sixty minutes in an hour therefore,

$8\textup{ hours }13\textup{ minutes}=8+\frac{13}{60}=8.216\overline{6}$

Step 3: Substitute in known values into the half life formula to solve for .

$A=150\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{8.216\overline{6}}{3.4}}$

$A=150\textup{ mg}\cdot \left(\frac{1}{2}\right)^{2.4166}$

$A=150\textup{ mg}\cdot 0.1873$

$A=28.09\textup{ mg}$

Report an Error

Example Question #4 : Growth And Decay By Contant Percent Rate: Ccss.Math.Content.Hsf Le.A.1c

An particular medicine, has a half-life of about hours. If a patient was administered $800 mg of the drug at $8:00 am , how much is left at $1:00 pm ?

Note: The half life formula is

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

Possible Answers:

$A=518.72\textup{ mg}$

$A=517.82\textup{ mg}$

$A=520.72\textup{ mg}$

$A=516.72\textup{ mg}$

$A=518.02\textup{ mg}$

Correct answer:

$A=518.72\textup{ mg}$

Explanation:

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the known values given in the question.

$A=A_0\cdot \left(\frac{1}{2}\right)^{\frac{t}{h}}$

$\\A_0=\textup{Intial Amount}=800\textup{ mg} \\h=\textup{half life}=8\textup{ hours} \\t_f=1:00\textup{ pm} \\t_i=8:00\textup{ am} \\A=?$

Step 2: Calculate .

$1:00-8:00\rightarrow 5 \textup{ hours }$

Step 3: Substitute in known values into the half life formula to solve for .

$A=800\textup{ mg}\cdot \left(\frac{1}{2}\right)^{\frac{5}{8}}$

$A=800\textup{ mg}\cdot \left(\frac{1}{2}\right)^{0.625}$

$A=800\textup{ mg}\cdot 0.6484$

$A=518.72\textup{ mg}$

Report an Error

View Tutors

Tawana
Certified Tutor

Ashford University, Master of Arts, Education.

View Tutors

Lilibeth
Certified Tutor

Cebu Institute of Technology, Bachelor of Science, Chemical Engineering.

View Tutors

Peter
Certified Tutor

Rutgers University-New Brunswick, Bachelor of Science, Computer Science.

All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

SAT Tutors in Houston, Statistics Tutors in San Francisco-Bay Area, Calculus Tutors in Atlanta, ACT Tutors in Chicago, LSAT Tutors in Atlanta, MCAT Tutors in Seattle, Math Tutors in Phoenix, MCAT Tutors in San Diego, Algebra Tutors in San Francisco-Bay Area, Spanish Tutors in Los Angeles

Popular Courses & Classes

MCAT Courses & Classes in Houston, SAT Courses & Classes in Houston, ISEE Courses & Classes in San Diego, GRE Courses & Classes in Atlanta, GMAT Courses & Classes in Phoenix, GRE Courses & Classes in Denver, ISEE Courses & Classes in Denver, ISEE Courses & Classes in Philadelphia, SSAT Courses & Classes in Seattle, GMAT Courses & Classes in Miami

Popular Test Prep

GRE Test Prep in Miami, ACT Test Prep in Denver, LSAT Test Prep in Miami, SSAT Test Prep in San Diego, SSAT Test Prep in Phoenix, ISEE Test Prep in San Francisco-Bay Area, GMAT Test Prep in Los Angeles, SSAT Test Prep in New York City, SSAT Test Prep in Boston, MCAT Test Prep in Chicago

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

Common Core: High School - Functions : Growth and Decay by Contant Percent Rate: CCSS.Math.Content.HSF-LE.A.1c

Study concepts, example questions & explanations for Common Core: High School - Functions

All Common Core: High School - Functions Resources

Example Questions

Example Question #21 : Linear, Quadratic, & Exponential Models*

Example Question #22 : Linear, Quadratic, & Exponential Models*

Example Question #23 : Linear, Quadratic, & Exponential Models*

Example Question #24 : Linear, Quadratic, & Exponential Models*

Example Question #25 : Linear, Quadratic, & Exponential Models*

Example Question #26 : Linear, Quadratic, & Exponential Models*

Example Question #1 : Growth And Decay By Contant Percent Rate: Ccss.Math.Content.Hsf Le.A.1c

Example Question #2 : Growth And Decay By Contant Percent Rate: Ccss.Math.Content.Hsf Le.A.1c

Example Question #3 : Growth And Decay By Contant Percent Rate: Ccss.Math.Content.Hsf Le.A.1c

Example Question #4 : Growth And Decay By Contant Percent Rate: Ccss.Math.Content.Hsf Le.A.1c

All Common Core: High School - Functions Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: