Defining Homeland Security Example

Defining Homeland Security Example Defining Homeland Security – Coursework Example Defining homeland security Homeland security is a collective term that refers to the government’s effort to keep the country secure, safe and resilient against both acts of terrorism and other hazards. The Department of Homeland Security carries out the above mandate thereby safeguarding the country and its territories. The department does this by carrying out surveillance with the view to averting acts of terrorisms, responding to terror attacks thereby minimizing casualties. The department does the same to both natural and man-made disasters that threaten the security and safety of the homeland. The department carries out an extensive surveillance on the country and its territories. However, claims of extravagance coupled with ineffectiveness are rife. The department spends extensively in protecting the country from an external enemy who may not exists thereby leaving the homeland vulnerable to homegrown problems. Current trends in terrorism show that school shootings by Ame ricans among other similar incidences are on the rise. Additionally, excessive use of force by the country’s police service has caused tens of deaths thereby polarizing the country. As the population remains divided, the country remains vulnerable to both external and internal aggression.In order to enhance the security and safety of homeland, the department must adopt a holistic approach by investing in nabbing internal threats as well as it does on external aggressions. The department must adopt a multi-agency approach in the fight against terror in order to ensure that it keeps the country safe from both internal and external aggressions. The department of homeland security must work alongside homeland defense by sharing intelligence but limiting its operations to homeland (U.S Department of Homeland Security, www.dhs.gov). This way, the department will enhance its effort in enhancing the safety and security of the country thus increasing the efficiency of its operations.W ork citedU.S Department of Homeland Security. National infrastructure protection plan. Washington, D.C: Government printing office, 2009. Internet resource. www.dhs.gov/xlibrary/assets/NIPP_Plan.pdf

Function Generator essays

Function Generator essays Purpose: The purpose of this experiment is to construct a function generator capable of taking a DC input and producing different outputs. The three desired outputs are a sinusoidal wave, a square wave, and a triangle wave. The function generator should also include a DC offset adjustment as well as amplitude control for the output waveform. Components to be used: DC power supply ( +15 Volts), 3 1N4148 diodes, one LED, 4 741 op-amps, 3 0.01 micro-farad capacitors, 2 1 micro-farad capacitors, 1k-ohm resistor, 2.2k-ohm resistor, 8.2k-ohm resistor, 10k-ohm resistor, 1 ganged 10k-ohm potentiometer, 2 10k-ohm potentiometers, 15k-ohm resistor, 2 18k-ohm resistor, 100k-ohm potentiometer. 1. Construct the Wein-bridge oscillator as shown in figure 1. Test output point A for sine wave, adjust potentiometers to change amplitude and frequency. 2. Construct the Schmitt trigger shown in figure 2. Connect input point A to output point A. Test output point B on the Schmitt trigger, the output should be a square wave. 3. Construct the integrator shown in figure 3. Connect input point B to output point B. Test output point C on the integrator, the output should be a triangle wave. 4. Construct the circuit shown in figure four. Adjust the potentiometer to adjust the DC offset. Discussion of Results: By following the above procedure, you should develop the desired function generator. The end result should match figure 5. Along the way a couple of problems were encountered. First, by using a 741 op-amp in the second stage (Schmitt trigger), a perfect square wave could not be obtained. By substituting a 318 op-amp it corrected the problem. The 318 gave a cleaner output because of its higher slew rate. The other problem occurred in the third stage, the integrator. The output of this stage using the called for capacitor (0.047 micro-farads) gave a distorted output. By adding a ...

The Duties Owed by Agents to their Principals May or May not be Essay

The Duties Owed by Agents to their Principals May or May not be Dictated by the Express Terms of the Contracts Between them - Essay Example (2011). Q & A Commercial Law 2011-2012. Oxon: Taylor & Francis 6th ed. De Busccche v Alt (1878) 8 ChD 286 in Reddy, J., & Johnson, H. (2011). Q & A Commercial Law 2011-2012. Oxon: Taylor & Francis 6th ed. Headley Byrne & Co ltd v Heller & Partners Ltd (1964) AC 465 in Reddy, J., & Johnson, H. (2011). Q & A Commercial Law 2011-2012. Oxon: Taylor & Francis 6th ed. Robinson v Mollett (1875) LR 7 HL 802 in Reddy, J., & Johnson, H. (2011). Q & A Commercial Law 2011-2012. Oxon: Taylor & Francis 6th ed. Solley v Wood (1852) in Reddy, J., & Johnson, H. (2011). Q & A Commercial Law 2011-2012. Oxon: Taylor & Francis 6th ed. Turnbull v Garden (1869) 20 LT 218 145 in Reddy, J., & Johnson, H. (2011). Q & A Commercial Law 2011-2012. Oxon: Taylor & Francis 6th ed. Turpin v Bilton (1843) 5 Man & G 455 in The Law of Agency, The Law of International Trade and Carriage of Goods. Accessed 2 Nov 2011 Watteau v Fenwick [1893] 1 QB 346 in University of London External Programme Accessed 2 Nov 2011 Weigal l& Co v Runciman & Co (1916) 85 LJKB 1187 in Munday Roderick and Munday R.J.C. LJKB 1187 Agency; Law and Principles (2009) Oxford, Oxford University Press The duties owed by agents to their principals may or may not be dictated by the express terms of the contracts between them Agency is an exception to the doctrine of privity in a contract in that a principal is bound by all acts of his agent by virtue of an agreement between him and the agent. Both law and specific terms of contract between them govern the duties owed by agents to their principals. Although a contract of agency is subject to the same rules as in any other contracts, there are certain terms implied such as fiduciary relationship between the principal and the agent which gives rise duties owed to the principal by the agent and rights he can exercise against the principal. In addition, a type known as ‘commercial agent’ also is subject the Commercial Agents (Council Directive) Regulations 1993 pursuant t o European Union Law dealing with termination of agreement in respect of self-employed agents who arrange contracts for the sale or purchase of goods. As per these regulations, a duty is cast on the agents to act ‘dutifully and with good faith’ which term cannot be contracted out by a separate contract between them. Even in the case of gratuitous acts of an agent where there can be no contractual obligations, the agent has fiduciary duties which cannot be avoided merely because of lack of consideration. He will also be liable under torts. In Watteau v Fenwick (1893), hotel owner was held liable for the price of cigar bought by the manger who had been instructed not to buy other than mineral water and beer. This decision is still controversial since the agent acted against the instructions though the supplier assumed that the manager was the owner (Reddy & Johnson, 2011) (Sealy, Hooley, & Hooley, 2008). An agent’s duties regardless of the contractual terms between him and the principal are as follows. Duty to obey All lawful instructions of the principal must be obeyed by his agent. He should not also exceed his authority. This is applicable to both paid and gratuitous agent categories. However, if the instructions are not

Human Resource Development in UK Essay Example | Topics and Well Written Essays - 1750 words

Human Resource Development in UK - Essay Example As manpower is cheap in developing countries, these countries could concentrate on providing training for jobs that do not require such high skills. Similarly, there are developing countries that wish to compete with the advanced countries in producing specialized goods and services. To produce high-technology products would require the necessary arrangements and investments for long term research along with expensive and complex production equipment. However, providing the right environment for the skilled human resources would make them perform better. For a job to be done well, not only is a person required to have inherent talent, but also be provided with the latest skills in that particular industry. Sometime, they can be made to have the skill by hiring them from outside the organisation. But it is difficult to achieve this by training and developing the present employees. Human Resource Development (HRD) is a planned curriculum that is used in order to invest in human capital. Development of human resources is one of the most important contributors to the success of the UK economy. It draws on other human resource processes, for example resourcing and performance evaluation, so that the real and probable talent can be recognized. HRD helps to present a structure for self-development, training courses and career progression. We will recover in the following HRD at the environmental level, HRD and the organization, the learning organization, Development programmes, induction, Empowerment and HRD and Leadership development. HRD at the environmental level In order to respond to the changing demands of the job market, human capital development should be in the form of education and skills training. Some skills are a rarity even when there is high employment. Newswire Today reports that in 2007 a report was issued by the British Chambers of Commerce (BCC) entitled "UK Skills: Making the Grade". This report was based on a survey of over 300 employers in the UK. According to this report, 55% of the employers who were evaluated were finding it more difficult to employ skilled workers now as compared to the five years ago. In order to find a solution to this problem, in the same year the UK Government announced the major expansion in skills investment for England of over 11 billion for each of the next three years. The total spending on learning and skills is likely to increase to 12.3 billion in a year by 2010/11. This is comparing with the 6.5 billion spent in 2001/02 (Department for Innovation, Universities & Skills, n.d.). There are many differences in education and training levels in the many countries around the world. For example, in Germany, they consider technology and production as high status activities. In their opinion, to succeed in some areas, employees must have a high level of technical training. Thus German businesses give greater importance to technical advantage than those in the UK. In the UK, it is not only technology that is important but other areas as well, even the ones unconnected to the engineering and technical side. A case in point could be the Film Industry in Britain. It is only recently that the Film Industry has been credited, but it is a fact that the UK has tried to make it successful. For this purpose, the Film Industry

Education School Essay Example for Free

Education School Essay Education is a topic that has been implemented on our generation more than ever before. However, it is not for the grades, degree or the income that education should be important to us. It is for the sake of learning and developing our character that education should be valued. When people go to school, they receive education and thus become educated, however, these people must keep in mind that a major portion of the world receives no form of formal education. Due to their good fortune, the educated people have responsibilities to the world. The first responsibility of an educated person is to help educate others. This may come in the form of teaching classes, tutoring, helping others or simply correcting errors. When we teach people we spread the value of education and share skills that are essential for survival. Other people are able to think rationally and evolve into a self dependent person through the knowledge they attain. Once people are educated, they are able to prevent others from taking advantage of them or cheating them. Through education, people are also able to use the resources they own efficiently and sparingly. Finally, education allows people from different nationalities and locations to communicate and work together in a beneficial harmony. The second responsibility of an educated person is to aim to advance to a better future. It is through evolution that we have become more intellectual and learned. For this process to be beneficial and continuous, we must use it and upgrade it through our use. In the past, communication was a problematic process, today; we have e-mail accounts, cell phones, chat sites, video chat sites and messengers for instant communication. Presently, global warming and oil depletion are major complications. If we are able to advance and address this problem, we would be using our education beneficially. There would be less violence over oil and the future would be a less worrisome place if global warming was tackled. However, this is just one amongst the billions of changes we could make, all to create a better future. The third responsibility of an educated person is to create or maintain stability and order in the world. Through stability and order, the world  becomes a much safer place where people share respect for each other and live in harmony. When there is order, people are insured of payments for their services. They are motivated to work-hard and use positive, instead of negative means to earn their income. Thus, through stability and order, ethics can also be implemented into people. Thus, the three main responsibilities of an educated person are to educate others, aim for a better future and create as well as maintain stability in the world. Through these goals, the world becomes a positive place and continues to flourish after each generation.

James Baldwins Story Sonnys Blues Essay -- James Baldwin Sonnys Blu

James Baldwin's Story Sonny's Blues James Baldwin?s story ?Sonny?s Blues? is a deep and reflexive composition. Baldwin uses the life of two brothers to establish parallelism of personal struggle with society, and at the same time implies a psychological process of one brother leaving his socially ingrained prejudices to understand and accept the other's flaws. The story is narrated by Sonny?s older brother whom remained unnamed the entire story. Sonny's brother is a pragmatic person, a teacher, husband, and father. He is a typical middle class Joe whose life?s purpose is to conform to society?s rules. He is a conservative person who seldom takes risks, and accepts the majority?s judgment over his. Sonny?s brother has assimilated into white society (mainstream) as much as possible, but still angers at institutional discrimination and the limits placed upon his opportunities. Contrastingly, Sonny has never tried to assimilate any model. He is looking to vent the deep pain and suffering that his status as permanent outsider confers upon him. Both brothers grew up in Harlem (this story elapses from the early 50?s to late 60?s), surrounded by parents carrying psychological scars of discrimination and struggle. Is here at the family?s nest where the brother?s personalities started to split: though the narrator and his parents are physically there for most of Sonny?s childhood, they never really hear him or listen to him, so Sonny drew himself inwards, with disdain for social rules. Sonny?s older brother saw himself as the one bound to take the helm at the light of his father drunkenness. After their parent?s death, Sonny is propelled by his older brother to stay with Isabel?s family (Sonny?s brother?s wife), an effort of Sonny?s brother to rail him into social conformity. Sonny is desperately trying to express himself, first, by telling his brother his wishes to become a Jazz musician, second, through music, restlessly practicing piano lessons at Isabel?s house. Neither Sonny?s brother nor Isabel?s family understand him. So he seeks more of his kind. He runs out the house, joins the navy, travels for a while, and comes back to New York as a Jazz pianist. Sonny?s brother, following a conservative path, uses denial as mechanism of defense. He refuses to accept Sonny for what he is: ?I didn?t like the way he carried himself, loose and dreamlike ... ...r has, as a ?real musician.? In the nightclub?s environment he is the unfit. When music starts to be played, he begins to understand the language of Jazz; the way in which it helps artists express their torment and their fear. While Sonny was performing, he feels how Sonny?s pain and suffering was exiting his body through his finger tips to the piano?s ivory, to the wooden hammers, to the piano wires, and finally airborne in music notes engulfing everybody as communion between the performer and the audience. Sonny internalizes and then expresses all the anguish and joy of the audience. When the music stops, older brother was in tears, because Sonny?s music also made him go deep inside himself and find the pain of his daughter?s death; the pain of broken promises, and the pain of denying his own kind. The end is a triumph for both: Sonny showed his brother his world, his purpose, his bitter-sweet happiness, even with the always present lure of addiction. Older brother found respect and acceptance for Sonny, and such acceptance transformed his view of everything around him. Works Cited: Baldwin, James. "Sonny's Blues" in Vintage Baldwin. New York: Vintage, 2004.

Religion, Morality, and the Good Life

Religion, Morality, and the Good Life Does morality depend on religion? Many believe the fundamental aspects of morality and religion join to form the basis on how one chooses to live their life. Some would define morality as a system we humans use to distinguish between what is right and what is wrong. Morality could derive from a number of different factors including, religion, culture, and upbringing. Those that believe that morality derives from religion or God’s commands trust in the Divine Command Theory.The Divine Command Theory is the idea that morality is dependent on God; that one’s moral obligation be determined by their obedience to God’s commands. This theory has been and probably will continue to be controversial to many. Morality must have a purely secular foundation. Although religion might not be the concrete basis for morality, it is certain that religion is needed sometime when dealing with specific aspects of morality. There are 2 types of mor ality, justified and unjustified. Justified morality is common sense and does not require intense interpretation.For example, â€Å"Do not steal† is a justified moral command because when one steals they are bringing evil to someone and that is immoral. Unjustified morals are much harder to find reason for than justified morals which can be easily justified by common knowledge. â€Å"Do not have sex before marriage,† is an example of an unjustified morality. It is difficult to explain why doing the act is immoral. This moral standard is irrational in that there is no reasonable answer why one should not do this act in order to remain moral.Religion comes in handy when dealing with grey areas of morality. Those grey areas are known as the unjustified moral commands or unjustified morality. Given the example for an unjustified moral command, one could answer the question â€Å"Why should I not do this in order to remain moral,† by saying it is immoral to have sex before marriage because God commanded us not to because he will punish one who does not follow his commandments. There is no central harm because if this action but one’s self-interest or fear of God’s wrath will keep one from committing this immoral act.The use of God and religion to justify these issues is only useful when dealing with a God-fearing and moral person. Although using religion with morality, in this case, may cause one to agree that morality needs religion and that the Divine Command Theory explains why, it does not justify that religion is the basis for morality. Are right and wrong actions commanded by God? The Divine Command Theory states that good and bad are created by God, not by humans. It has been illustrated that the Divine Command Theory cannot be logically true.The Divine Command Theory states that if God commands â€Å"A,† his commands by itself are sufficient to make â€Å"A† good. â€Å"A is good† just means â€Å"A i s commanded by God. † God’s commands are good simply because God commands it. If there were no God, or if God did not issue any commands, then there would be no such thing as moral right or wrong. However, if actions are good on their own without influence from God, then the Divine Command Theory is false because it is naturally commanded that we do things which are good and avoid those in which we know to be wrong.One’s belief in the existence of a god or gods may cause one to believe that morality assumes God’s existence. Their beliefs seem to give their lives purpose and clear understanding. In Genesis 1:27 it says, â€Å"So God created mankind in his own image, in the image of God he created them; male and female he created them. † (NIV) According to Christianity, God created us in his likeness as to fulfill the plan or purpose that he had intended for us. With this idea, the Catholic Church developed the concept of natural law.This natural law concept stated that by working out what one’s purpose is, we will be able to see how we should act and/or behave; it would be apparent in the way in which we have been designed. Within the Catholic Church, the Pope’s condemnation of homosexuality is an example of the natural law theory at work. The natural result to sex is conception, and any other sexual act that is not available to this possibility would be an immoral rejection to the plan God had intended for them. It is obvious that this natural law approach to ethics can cause controversy.It might be perceived as a poor imitation of morality in that it fails to provide justification for many basic moral principles. The supposed link between God and morality provides the idea because God is omnipotent and our creator; we have an obligation to obey his commands. With him being our creator, we owe him our existence. Many ask the obvious question, â€Å"Why do we have this obligation? † Although this view has n ot stood up to reflection, people once believed that children owed the act of obedience to their parents only because children depended on their parents. This view is remarkably similar to the reasoning given for feudalism.In feudalism, in exchange for the protection of the lord, the vassal would give some sort of service to the lord. The obligation between the lord and the vassal regarding the fief or land forms the basis of the feudal relationship. The weakness in this political system was that the vassals never agreed to this plan. By answering the above question in saying that our obligation to obey God’s command is because obedience is morally right, the assumption has been made that morality exists independently of God. Why things are right in the first place is justified and explained by the Divine Command Theory.The Divine Command Theory shows an apparent resemblance to the natural law approach as discussed just before. Rather than focusing on features of his assumed creation as with the natural law theory, the Divine Command Theory implicates a focus on God’s orders. An obvious example of God’s orders would be the Ten Commandments. The most common objection to this approach is that it makes morality seem somewhat subjective. It implies the theoretical likelihood of rape being right simply because God commands this. Some may say that God would never command such an act as rape. God has not, in fact, commanded that rape is good.Assuming that the Divine Command Theory is, in fact, true, it would see God’s goodness in that he will not do anything wrong. But it does not follow that he won’t be unjust or cruel. As long as he is not violating any of his commands, no matter what God does, he will not be doing anything wrong. God is omniscient and morally perfect. Surely this gives us exact reason to why we ought to obey his commands. God’s moral perfection, after all, guarantees that he will issue only those commands that he thinks are right. His overall insight and expertise assures that he will never be wrong in what he believes is right to command of us.It sees God as the highest possible moral guide, giving us reason to always obey his commands. Although this is correct, it does not support the Divine Command Theory. To argue this point is to assume that the greater moral quality is dependent of God’s will, in which the basis for what he commands is. Some thinkers like Immanuel Kant and John Newman, just to name a few, have argued that a sense of conscience is evidence of God. With morality and religion being independent of one another, the independence is considered to be compatible with the existence of God.If we accept that the existence of conscience assumes a being to whom we owe responsibility, God would seem like the only candidate. He is the only person with omnipotent power to see and judge our every action. Newman furthered this thought by asking why people would feel guilty if they did not think they were being watched. In conclusion, there is something wrong with every way of linking morality to religion. I am not claiming that religion cannot have things to say about morality or that it is incapable of helping people do what is morally right.Instead, my claim is that ethics is enhanced with a religiously neutral foundation. Religion can be defined a set of practices independent of a belief system. Religion is the way in which you worship. Some people have participated in religious worship for a while without giving a great deal of thought to a belief system. Morality can be based on religion, but it also can be independent of one’s religion or faith. Although it is possible to hold a religion and not hold to any strong moral principles and vice versa for holding just moral principles, many people hold religious and moral principles.As with Christianity, religion is doing what you are told to do regardless of what is right, and morality is doi ng what is right regardless of what you are told to do. Although morality and religion are used at times to justify one another, they are not dependent of one another. . Works Cited â€Å"Genesis 1 NIV – The Beginning – In the beginning God – Bible †¦ † Bible Gateway. Web. 15 Apr. 2013 . â€Å"The Internet Classics Archive | Euthyphro by Plato. † The Euthyphro. N. p. , n. d. Web. 15 Apr. 2013

Paper cut

Dynasty, paper cuts have a close relationship with the custom activities and the drama (#5). People are likely to watch drama so that there are lots of dramas in that period of time. For instance, â€Å"The Romance of The West Chamber† Rid) is one of the drama in Yuan dynasty. People usually cut red paper into different characters with background according to the drama for different uses, they may sell them or use as decoration. During Mining and King Dynasty, paper cuts become common among ordinary people, paper cuts are common to see in different festivals such as autumn festivals and drama.On the other hand, paper cuts are widely used in decorating the indoor part of the palace. The paper cuts designs include Dragon, Phoenix, and Bat, and these designs are used to decorate the ceilings of the hall and the walls of the corridors . Up to now, paper cuts is losing its status in the society, people are unwilling to participate in the inheritance of paper cuts. People therefore have fewer opportunities to reach this kind of folk art but they still can find paper cuts at old laces and some traditional buildings.Traditionally, women and girls in the countryside have to take in charge of making embroidery, let alone, the paper cuts. This is used to be a craft that every women must know how to do in their life. It even uses this craft to distinguish whether the bride is good or bad. Every year, they usually take part in the making embroidery after the harvest period, while they have spare time, they will start doing paper cuttings in order to do preparation for the coming year. These paper cuts are used to decorate the windows

Blue Moon essays

Blue Moon essays The title of my book is Blue Moon. It was written by Susan Kirby and came from the series Life at Sixteen. Blue Moon has two hundred and two pages. This book is about Deanna Findley* and her next door neighbor who is also her best friend, Michael McKinsey*. Deanna is a high school junior who doesnt care about her looks or if she is in the in crowd, but cares more about her family and friends and their welfare. Formerly know as Dee she is a happy go-lucky girl who is slim, has brown hair and loves to baby-sit her younger brother, Doug. Dees importance in this book is that she helps Michael deal with his grandfathers illness and deals with her own family problems. Michael, Dees next door neighbor and secret crush, is tall, dark complected, and a nice guy to hang out with. He is in the popular crowd in a way, but isnt stuck up. The other characters in this book are Dees brother, Doug, a rambunctious, funny, caring, nine-year-old. This book containing also Alice, Dees sister, a thirteen year-old just discovering boys and having a hobby of being a brat to her little brother. Also among other characters are Mr. and Mrs. Findley (Dee s parents), Mrs. McKinsey (Michaels mother), and Mr. Kolupa (Michaels grandfather). The majority of the story takes place in Mayfield, a bustling central Illinois community of about thirty thousand residents. The neighborhood that Michael and Dee live in most of the houses are comfortable ranch-style homes that were built closely spaced. Some of the story takes place in Michaels grandfathers old shop across town. The end takes place in a nursing home called Rosewood. Mainly the story is in the spring and summer months, such as the last few days of school and throughout the summer. Blue Moon is a book about a young girl who gets out for the summer and notices changes in her beloved graduating friend. The changes really are ...

Exponential Functions - How to Find the Starting Value

Exponential Functions - How to Find the Starting Value Exponential functions tell the stories of explosive change. The two types of exponential functions are exponential growth and exponential decay. Four variables - percent change, time, the amount at the beginning of the time period, and the amount at the end of the time period - play roles in exponential functions. This article focuses on how to find the amount at the beginning of the time period, a. Exponential Growth Exponential growth: the change that occurs when an original amount is increased by a consistent rate over a period of time Exponential Growth in Real Life: Values of home pricesValues of investmentsIncreased membership of a popular social networking site Heres an exponential growth function: y a(1 b)x y: Final amount remaining over a period of timea: The original amountx: TimeThe growth factor is (1 b).The variable, b, is percent change in decimal form. Exponential Decay Exponential decay: the change that occurs when an original amount is reduced by a consistent rate over a period of time Exponential Decay in Real Life: Decline of Newspaper ReadershipDecline of strokes in the U.S.Number of people remaining in a hurricane-stricken city Heres an exponential decay function: y a(1-b)x y: Final amount remaining after the decay over a period of timea: The original amountx: TimeThe decay factor is (1-b).The variable, b, is percent decrease in decimal form. Purpose of Finding the Original Amount Six years from now, perhaps you want to pursue an undergraduate degree at Dream University. With a $120,000 price tag, Dream University evokes financial night terrors. After sleepless nights, you, Mom, and Dad meet with a financial planner. Your parents bloodshot eyes clear up when the planner reveals an investment with an 8% growth rate that can help your family reach the $120,000 target. Study hard. If you and your parents invest $75,620.36 today, then Dream University will become your reality. How to Solve for the Original Amount of an Exponential Function This function describes the exponential growth of the investment: 120,000 a(1 .08)6 120,000: Final amount remaining after 6 years.08: Yearly growth rate6: The number of years for the investment to growa: The initial amount that your family invested Hint: Thanks to the symmetric property of equality, 120,000 a(1 .08)6 is the same as a(1 .08)6 120,000. (Symmetric property of equality: If 10 5 15, then 15 10 5.) If you prefer to rewrite the equation with the constant, 120,000, on the right of the equation, then do so. a(1 .08)6 120,000 Granted, the equation doesnt look like a linear equation (6a $120,000), but its solvable. Stick with it! a(1 .08)6 120,000 Be careful: Do not solve this exponential equation by dividing 120,000 by 6. Its a tempting math no-no. 1. Use Order of Operations to simplify. a(1 .08)6 120,000 a(1.08)6 120,000 (Parenthesis) a(1.586874323) 120,000 (Exponent) 2. Solve by Dividing a(1.586874323) 120,000 a(1.586874323)/(1.586874323) 120,000/(1.586874323) 1a 75,620.35523 a 75,620.35523 The original amount, or the amount that your family should invest, is approximately $75,620.36. 3. Freeze -youre not done yet. Use order of operations to check your answer. 120,000 a(1 .08)6 120,000 75,620.35523(1 .08)6 120,000 75,620.35523(1.08)6 (Parenthesis) 120,000 75,620.35523(1.586874323) (Exponent) 120,000 120,000 (Multiplication) Practice Exercises: Answers and Explanations Here are examples of how to solve for the original amount, given the exponential function: 84 a(1.31)7Use Order of Operations to simplify.84 a(1.31)7 (Parenthesis) 84 a(6.620626219) (Exponent)Divide to solve.84/6.620626219 a(6.620626219)/6.62062621912.68762157 1a12.68762157 aUse Order of Operations to check your answer.84 12.68762157(1.31)7 (Parenthesis)84 12.68762157(6.620626219) (Exponent)84 84 (Multiplication)a(1 -.65)3 56Use Order of Operations to simplify.a(.35)3 56 (Parenthesis)a(.042875) 56 (Exponent)Divide to solve.a(.042875)/.042875 56/.042875a 1,306.122449Use Order of Operations to check your answer.a(1 -.65)3 561,306.122449(.35)3 56 (Parenthesis)1,306.122449(.042875) 56 (Exponent)56 56 (Multiply)a(1 .10)5 100,000Use Order of Operations to simplify.a(1.10)5 100,000 (Parenthesis)a(1.61051) 100,000 (Exponent)Divide to solve.a(1.61051)/1.61051 100,000/1.61051a 62,092.13231Use Order of Operations to check your answer.62,092.13231(1 .10)5 100,00062,092.13231(1.10)5 100,000 (Parenthesis)62,092.13231(1.61051) 100,000 (Exponent)100,000 100,00 0 (Multiply) 8,200 a(1.20)15Use Order of Operations to simplify.8,200 a(1.20)15 (Exponent)8,200 a(15.40702157)Divide to solve.8,200/15.40702157 a(15.40702157)/15.40702157532.2248665 1a532.2248665 aUse Order of Operations to check your answer.8,200 532.2248665(1.20)158,200 532.2248665(15.40702157) (Exponent)8,200 8200 (Well, 8,199.9999...Just a bit of a rounding error.) (Multiply.)a(1 -.33)2 1,000Use Order of Operations to simplify.a(.67)2 1,000 (Parenthesis)a(.4489) 1,000 (Exponent)Divide to solve.a(.4489)/.4489 1,000/.44891a 2,227.667632a 2,227.667632Use Order of Operations to check your answer.2,227.667632(1 -.33)2 1,0002,227.667632(.67)2 1,000 (Parenthesis)2,227.667632(.4489) 1,000 (Exponent)1,000 1,000 (Multiply)a(.25)4 750Use Order of Operations to simplify.a(.00390625) 750 (Exponent)Divide to solve.a(.00390625)/00390625 750/.003906251a 192,000a 192,000Use Order of Operations to check your answer.192,000(.25)4 750192,000(.00390625) 750750 750

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