Loading...

Messages

Proposals

Stuck in your homework and missing deadline? Get urgent help in $10/Page with 24 hours deadline

Get Urgent Writing Help In Your Essays, Assignments, Homeworks, Dissertation, Thesis Or Coursework & Achieve A+ Grades.

Privacy Guaranteed - 100% Plagiarism Free Writing - Free Turnitin Report - Professional And Experienced Writers - 24/7 Online Support

Linear automobile depreciation 5 5

22/11/2021 Client: muhammad11 Deadline: 2 Day

Lesson 4.2

Introduction

Course Objectives

This lesson will address the following course outcomes:

· 20. Translate problems from a variety of contexts into mathematical representation and vice versa (linear, exponential, simple quadratics).

· 23. Determine the exponential function for a situation when given an initial value and either the growth/decay rate or a second function value. Interpret the initial value and growth rate of an exponential function. Include compound interest as one application.

· 25. Use functional models to make predictions and solve problems.

Specific Objectives

Students will understand

· the differences and similarities between exponential growth and decay.

· the differences between linear and exponential growth

Students will be able to

· write an equation for an exponential decay model.

In this lesson, you will connect the exponential mathematics of compounding to related applications, such as automobile depreciation and spread of disease.

Depreciation

Problem Situation 1: Understanding Depreciation

Depreciation is a process of losing value, opposite to that of accruing interest. For example, new automobiles lose 15% to 20% of their value each year for the first few years you own them.

Suppose you purchase a a $26,000 automobile that depreciates 15% per year.

#1 Points possible: 5. Total attempts: 5

What will the value of the car be when it is 1 year old?

$

#2 Points possible: 5. Total attempts: 5

Think back to the last lesson, and how you came up with the general formula for the balance of the 5-year CD after t years.

Using the same idea, find a formula for the depreciated value (V) of this car after t years.

V =

Hint: If you get stuck, we'll offer some hints

#3 Points possible: 5. Total attempts: 5

Using the formula you just created, predict the value of the car after 5 years. Round to the nearest cent if needed.

$

#4 Points possible: 5. Total attempts: 5

If you were to graph the value of the car over time, which of the following graphs reflects what you would expect to see?

In the last lesson, you looked at compound interest which is an example of exponential growth. In the previous problem, depreciation is an example of exponential decay. Note the similarities and differences to the growth model.

· Both have a vertical intercept that represents the starting value and is in the equation.

· The base of the exponent in the growth model is >1. The base of the exponent in the decay model is between zero and one.

· Both the compound interest formula (exponential growth) and the decay model have the same basic form, y=Caxy=Cax , with a starting value (C) that is multiplied by a factor raised to a variable power. The base of the exponential is 1+growth rate1+growth rate for growth, and 1−decay rate1-decay rate for decay. Note that the general compound interest formula looks different, but the (1+rk)(1+rk) factor can be simplified down to one number.

· In growth, rate of change starts slow and increases. In decay situations, the rate of change initially represents a steep negative decline but becomes less steep (but still negative) as time goes on.

· Both are based on multiplicative (or relative) change.

Spreading Disease

Problem Situation 2: A Spreading Disease

During 2014, there was an Ebola breakout in West Africa. On April 1, 2014, there had been 130 cases reported. A month later there had been 234 cases reported.

#5 Points possible: 12. Total attempts: 5

Find the absolute and relative change between the two reported values.

Absolute change:

Relative change: As a decimal: . As a percent: %

#6 Points possible: 5. Total attempts: 5

Let C represent the number of cases after t months, so t = 0 corresponds to April 2014.

Find a formula for a linear model based on the data given, assuming the trend continues.

C =

Hint: If you get stuck, we'll offer some hints

#7 Points possible: 5. Total attempts: 5

Let C represent the number of cases after t months, so t = 0 corresponds to April 2014.

The relative change you found two questions earlier is the percent increase, or percent growth rate, during the month. Use it to find a formula for an exponential model based on the data given, assuming the trend continues.

C =

Hint: If you get stuck, we'll offer some hints

#8 Points possible: 10. Total attempts: 5

What does each model predict the number of cases to be after 6 months? Round to the nearest whole number.

Linear model: cases

Exponential model: cases

#9 Points possible: 10. Total attempts: 5

What does each model predict the number of cases to be after 2 years (24 months)? Round to the nearest whole number.

Linear model: cases

Exponential model: cases

Summary of Exponential Equations

In this lesson and the previous one you learned about exponential models. Exponential equations are used when a quantity is growing or decreasing by the same percent every time interval.

Exponential Equations

Exponential equations have the form y=P(1+r)ty=P(1+r)t

· y is the output variable

· P is the initial value, or vertical intercept (y-intercept)

· r is the percent growth rate (relative growth rate) written as a decimal

· If the quantity is growing, r will be positive

· If the quantity is decreasing, then r will be negative

· t is time

A special case of the exponential equation is the compound interest equation, which looks like A=P(1+rn)ntA=P(1+rn)nt , where n is the number of compounds in a year.

To find an exponential equation from given information:

· The initial value will be given. Identify it

· Is the percent growth rate given?

· If yes, identify it

· If no, then look for a second output value, and find the relative (percent) change

Example 1: A population is currently 30,000 and is growing by 4.2% per year.

· Initial population is P=30000

· Growth rate is r= 4.2% = 0.042

· Equation will be y=30000(1+.042)t=30000(1.042)ty=30000(1+.042)t=30000(1.042)t

Example 2: A car was purchased for $12000 and its value decreases by 8% each year

· Initial value is P=12000

· Growth rate is r= -8% = -0.08. Notice it is negative because it's decreasing in value

· Equation will be y=12000(1−0.08)t=12000(0.92)ty=12000(1-0.08)t=12000(0.92)t

Example 3: A biologist started with 200 bacteria in a dish, and in 1 hour the amount grew to 300. Find an exponential equation for the number of bacteria.

· Initial value is P=200

· We don't know the growth rate, so we'll find the relative change from 200 to 300: 300−200200=100200=0.5300-200200=100200=0.5 . So the growth rate is 50% = 0.5.

· Equation will be y=200(1+0.5)t=200(1.5)ty=200(1+0.5)t=200(1.5)t , where t is in hours.

HW 4.2

#1 Points possible: 5. Total attempts: 5

Which of the following was one of the main mathematical ideas of the lesson?

· Cars lose value quickly after purchase.

· Multiplying a number by a second number between 0 and 1 will give you a larger number than you started with.

· All exponential models share certain characteristics such as the general shape of the graph, increase or decrease by a percentage, and having a vertical intercept.

· Depreciation can be modeled with an exponential equation.

#2 Points possible: 8. Total attempts: 5

One way to describe a linear model is that it is based on additive change while an exponential model is based on multiplicative change. Complete the sentences below illustrating why these terms apply to each model.

In the linear table below, each time x increases by 1, we .

In the exponential table below, each time x increases by 1, we .

y = 2x+1

x

y

0

1

1

3

2

5

3

7

4

9

y = 3(2)x

x

y

0

3

1

6

2

12

3

24

4

48

#3 Points possible: 12. Total attempts: 5

Select the letter of each graph next to the equation that best matches it.

y = 1,000(0.95)x y = 200 + 11x y = 5(1.1)x

http://s3.amazonaws.com/wamapdata/ufiles/2/4-1-6-3.jpg

#4 Points possible: 15. Total attempts: 5

Certain drugs are eliminated from the bloodstream at an exponential rate. Doctors and pharmacists need to know how long it takes for a drug to reach a certain level to determine how often patients should take medications. Answer the following questions about this situation.

a. Select the correct statement:

· More of the drug will be eliminated in the first hour than in the second hour.

· Less of the drug will be eliminated in the first hour than in the second hour.

· The same amount of the drug will be eliminated in the first hour as in the second hour.

b. Write an exponential equation for the following situation. The drug dosage is 500 mg. The drug is eliminated at a rate of 5.2% per hour. Use D = the amount of the drug in milligrams and t = time in hours.

c. How much of the drug is left after 6 hours? Round to the nearest milligram. milligrams

#5 Points possible: 18. Total attempts: 5

In Lesson 1.2, you looked at historical data of the world's population. Scientists use models to project population in the future. While these models have limitations, they help leaders plan ahead for the resources people will need. The World Bank estimates that that the world population growth rate in 2010 was 1.1%. The U.S. Census Bureau estimated the world population in 2010 to be about 6.9 billion people.2

a. This is an exponential situation because the population is increasing each year by a percentage of the previous year. Complete the table below based on the growth rate of 1.1%. Some of the entries are done for you. Round projected populations to 2 decimal places.

Calendar Year

Number of Years after 2010

Projected Population

2010

0

6.90 billion

2011

1

billion

2012

billion

2013

billion

b.

c. Write an exponential equation for the world population growth after 2010. Let P = the projected population in billions and t = the number of years after 2010. Hint: Think about how you calculated the entries in the table. If you started with 6.9 billion each time, how could you calculate each population? Think back to your work in the lesson.

d. Use your model to predict the population in 2020. billion

#6 Points possible: 10. Total attempts: 5

The Center for Disease Control (CDC) published the following information about respiratory disease in children. Respiratory disease is an illness that affects a person’s ability to breathe and use oxygen.3

In 2005, approximately one fourth of the 2.4 million hospitalizations for children aged < 15 years were for respiratory diseases, the largest category of hospitalization diagnoses in this age group. Of these, 31% were for pneumonia, 25% for asthma, 25% for acute bronchitis and bronchiolitis, and 19% for other respiratory diseases, including croup and chronic disease of tonsils and adenoids.

a. Based on this information, how many children were hospitalized for pneumonia in 2005? children

b. Which of the following pie charts accurately represents the data for children hospitalized for respiratory diseases?

https://s3.amazonaws.com/wamapdata/ufiles/2/4-1-5-8a.jpg https://s3.amazonaws.com/wamapdata/ufiles/2/4-1-5-8b.jpg https://s3.amazonaws.com/wamapdata/ufiles/2/4-1-5-8c.jpg

#7 Points possible: 15. Total attempts: 5

A ball is placed at the top of ramp and released. It's height above ground over time is shown in the table below.

Time (seconds)

Height (cm)

0

10

1

9

2

6

3

1

a. Plot the points from the table.

Height (cm)

Clear All Draw: Dot

Time (sec)

b.

c. Is this a linear model? Why or why not?

Is this an exponential model? Why or why not?

Homework is Completed By:

Writer Writer Name Amount Client Comments & Rating
Instant Homework Helper

ONLINE

Instant Homework Helper

$36

She helped me in last minute in a very reasonable price. She is a lifesaver, I got A+ grade in my homework, I will surely hire her again for my next assignments, Thumbs Up!

Order & Get This Solution Within 3 Hours in $25/Page

Custom Original Solution And Get A+ Grades

  • 100% Plagiarism Free
  • Proper APA/MLA/Harvard Referencing
  • Delivery in 3 Hours After Placing Order
  • Free Turnitin Report
  • Unlimited Revisions
  • Privacy Guaranteed

Order & Get This Solution Within 6 Hours in $20/Page

Custom Original Solution And Get A+ Grades

  • 100% Plagiarism Free
  • Proper APA/MLA/Harvard Referencing
  • Delivery in 6 Hours After Placing Order
  • Free Turnitin Report
  • Unlimited Revisions
  • Privacy Guaranteed

Order & Get This Solution Within 12 Hours in $15/Page

Custom Original Solution And Get A+ Grades

  • 100% Plagiarism Free
  • Proper APA/MLA/Harvard Referencing
  • Delivery in 12 Hours After Placing Order
  • Free Turnitin Report
  • Unlimited Revisions
  • Privacy Guaranteed

6 writers have sent their proposals to do this homework:

Accounting & Finance Master
Top Class Engineers
Fatimah Syeda
Innovative Writer
Financial Hub
Instant Assignment Writer
Writer Writer Name Offer Chat
Accounting & Finance Master

ONLINE

Accounting & Finance Master

I am a professional and experienced writer and I have written research reports, proposals, essays, thesis and dissertations on a variety of topics.

$32 Chat With Writer
Top Class Engineers

ONLINE

Top Class Engineers

I am an academic and research writer with having an MBA degree in business and finance. I have written many business reports on several topics and am well aware of all academic referencing styles.

$47 Chat With Writer
Fatimah Syeda

ONLINE

Fatimah Syeda

I have read your project description carefully and you will get plagiarism free writing according to your requirements. Thank You

$46 Chat With Writer
Innovative Writer

ONLINE

Innovative Writer

I have done dissertations, thesis, reports related to these topics, and I cover all the CHAPTERS accordingly and provide proper updates on the project.

$46 Chat With Writer
Financial Hub

ONLINE

Financial Hub

I am an elite class writer with more than 6 years of experience as an academic writer. I will provide you the 100 percent original and plagiarism-free content.

$18 Chat With Writer
Instant Assignment Writer

ONLINE

Instant Assignment Writer

I am a PhD writer with 10 years of experience. I will be delivering high-quality, plagiarism-free work to you in the minimum amount of time. Waiting for your message.

$23 Chat With Writer

Let our expert academic writers to help you in achieving a+ grades in your homework, assignment, quiz or exam.

Similar Homework Questions

Colonel reb is crying youtube - Organizational culture and readiness assessment tool for ebp - Elearning epsom and st helier - Reflection - Monash council abandoned cars - Discussion essay - How to create non objective art - Assignment 1 - Cdu allsp - Melton library opening hours - Kelvin hall school hull - How does a hovercraft work - Poem barbie doll marge piercy analysis - Ndis payment request rejected - Roll of thunder hear my cry characters pictures - Witch of agnesi parametric equation - I never saved anything for the swim back meaning - Are rolled oats acidic or alkaline - Covidien pulse oximeter manual - Hurricane sandy barometric pressure - Matrix of Ethical Theories - The boy in the striped pajamas chapter 8 - 5/15 dinmore street moorooka - Harvard business school matching dell case study - Siemens masterdrive parameter list - Use two articles from the PICOT question apart from the two you used in last week work - Star wars ccg red 5 - 8st 9lbs in kg - North american crew utilization 2016 - Tool with killing joke tickets little caesars arena november 9 - How do we express culture - One of the major goals of reality therapy involves - Ib extended essay rubric - Re-write - Cujo dog minding darwin - The prince by niccolo machiavelli answers - The right thing to do 8th edition pdf - Aftab iqbal family background - Https lc ugrad1 gcu edu - Ksf dimensions band 7 - Punchline algebra book b 14.4 answers - Front windshield defroster kit - Heritage assessment paper - Vocabulary rubric for words - Assignment - Online news stuart allan - Thor hanson feathers sat answers - Verbs of like and dislike - Dpp v smith 1961 - Tesco case study questions and answers - Aqa gcse english literature specification - Annual Report - Kmspico portable win 10 - Responsibility center example in healthcare - Algebra 2 assignment answer key - Which of the following is an online library penn foster - Does pof have a video call feature - MC Charts - Operational Excellence - Flinders university site map - Global minimum variance portfolio excel - Community And Nursing (Due 24 Hours) - Mexican white boy study guide - Mil g 81827 equivalent - A3 project plan template - Hegel's preface to the phenomenology of spirit - Zat you santa claus - Katherine mary knight husband - General survey nursing assessment example - C12 105da century agm battery price - History of graphic design ppt - Uni sa orientation week - Capstone goals and objectives - Leadership is the ability to ______ employees to voluntarily pursue organizational goals. - Verilog less than or equal - Liberal credit policy - Mi rutina diaria powerpoint - What is a balance day adjustment - Chaucer uses the pilgrimage primarily as a device to - 632wk3A3 - Informatics in healthcare - A batch of 500 containers for frozen - Quantitative techniques in management - Hp12c platinum vs gold - UI DEVELOPER - Campaign Project: Research and Planning - 1000 books before school nsw - Summary Assignment - Schmitt trigger oscillator op amp - Timmco Case Study - Grand canyon university lesson plan template - Media and culture 9th edition - Deriving value from social commerce networks - Which itil process uses mean time between failures mtbf - Dot matrix led display circuit diagram 8 32 - Neurological assessment pupil reaction - American eagle public relations - Accommodation near rockhampton hospital - IT - HR (MANA APRCH/MRKT U_4_RPL)