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DIRECTIONS AND ANALYSIS

UNIT:FUNCTIONSDIRECTIONS AND ANALYSISTask 1: Saving for Vacation

Jerry plans to begin saving money for a trip by putting $1 in a savings account the first month and then adding enough to double the amount in the account each following month.

After he finishes contributing to the account, he will withdraw $500 to make a down payment on the trip. Create a function to show how much money will be in the account if he finishes contributing to the account after t months.

Answer

A tabulation of some the saving pattern.

Month Amount Deposited Total Balance

1 1 1

2 1 2

3 2 4

4 4 8

5 8 16

6 16 32

7 32 64

The total balance follows the pattern 1,2,4,8,16,32,64…

It behaves similar to a geometric sequence with common ratio r=2 and first term a=1.

An=arn-1At=1×2t-1 for t=1,2,3,4,5…At=2t-1 for t≥1Jerry plans to keep up this saving pattern until he can no longer afford it. At that time, he hopes to have enough in his account for his trip. How much will be in the account, after making the down payment, if the most he will be able to contribute in a month is $1,200?

Answer

The maximum he can be able to contribute in a month is 1200 and at such a time the account will have 2×1200 since his deposit must double the amount.

Thus

At=2t-1=2×12002t-1=2400log2t-1=log2400t-1log2=log2400t-1=log2400log2t=1+log2400log2t=1+log2400log2t=1+11.23t=12.23Since at t=12.23 months he can add the maximum possible amount which is 1200 we need to round down to t=12 months to make sure he doesn’t surpass his ability.

Thus t= 12 months

A12=212-1=211=2048Balance after down payment

2048-500=1548Jerry’s friend Brandon is planning to start saving for a trip at the same time as Jerry. The graph shows the balance in Brandon’s account over the first few months of saving. Whose account will have the greatest balance after the first five months of savings, Brandon’s or Jerry’s?

Answer

Brandon saving pattern takes the form of a straight line

y=mx+cwhere the gradient m=∆y∆x=300-04-0=75and c=0ABt=75tAt t=5 months

AB5=75×5=375AJ5=25-1=24=16Thus Jerry’s account will have the greatest balance after the first five months of saving.

How long will it take for the person with the smaller account balance after five months to have the greater balance?

Answer

We need to get the time that Jerry will require to achieve Brandon’s amount at 5 months.

AJt=2t-1=375log2t-1=log375t-1log2=log375(t-1)=log375log2t=1+log375log2t=1+8.55t=9.55 monthsBrandon will also need to withdraw $500 to make a down payment on the trip. How much will be in Brandon’s account, after making the down payment, if he contributes for same amount of time as Jerry? (Review your calculation in part b to determine how long Jerry continued his savings plan.)

Answer

Amount for Brandon after 12 months.

ABt=75tAB12=75×12AB12=900Balance after down payment

900-500=400Task 2: Driving

Jerry is driving to his vacation destination. He decided to keep track of the distance to his destination after different amounts of times spent driving. He created a table from the data he collected.

Hours Spent Driving 1 5 6 9

Miles to Destination 1,259 999 934 739

Assuming that the pattern is the same for Jerry’s entire drive to his destination, create a function to represent the distance remaining to his destination based on the number of hours, h, he has driven.

Answer

f1=1259;f5=999;f6=934;f9=739Rate of change of distance per hour for the different intervals.

for 1-5 hrs=999-12595-1=-65for 5-6 hrs=934-9996-5=-65for 6-9 hrs=739-9349-6=-65Clearly the modelling function will be a straight line of gradient m=-65

y=mx+cWhere c is the total distance from origin to destination which occurs at h=0.

From 5-6 hrs it can be observed he covers 999-934=65 miles in an hour.

At 1 hr distance =1259

Thus

total distance=1259+65=1324 miles∴fh=-65h+1324What is the domain of this function in the context of the problem? Explain.

Answer

The domain will be the set of values which when plugged into the function will give the reasonable outputs between 0 to 1324 miles which the distance from Jerry’s origin to destination.

And

h≥0 since there are no negative hoursThe upper bound for the domain will be the time he takes to cover the whole journey when he gets at the destination.

fh=0=-65h+1324-65h=-1324h=-1324-65h=132465∴The domain is:0≤h≤132465What is the range of this function in the context of the problem? Explain.

Answer

This the set all possible outputs of the function for the given domain.

f0=-650+1324=1324f132465=-65132465+1324=-1324+1324=0∴The range is:0≤f(h)≤1324This the range of the distance from the origin to the destination.

When Jerry recorded the last entry in the table (9 hours driven, 739 miles to go), how much longer did he need to drive to arrive at his destination?

Answer

At the destination

fh=0=-65h+1324-65h=-1324h=-1324-65=132465 hrsHe needed

132465-9=73965hrs to complete the journey≈11.369 hrs(3 decimal places)Resources HYPERLINK “https://www.varsitytutors.com/hotmath/hotmath_help/topics/domain-and-range”

Varsity Tutors, “Domain and Range,” https://www.varsitytutors.com/hotmath/hotmath_help/topics/domain-and-range.

James Stewart, Essential Calculus, 2nd edition, Cengage Learning, 2012.

To what extent can the period in Britain between 1780 and 1914 be termed correctly as an industrial revolution

First and foremost, the industrial revolution, exacerbated by the increase in production of cotton in the North-West after the 1770’s and the invention of Arkwright’s water-frame, swelled the physical constitution of the population and began a permanent migration away from the countryside to the towns as a result of industry gradually usurping agriculture as the lifeblood of the nation. Liverpool, for example, was seventh in the list of European capital cities by 1850 with Manchester ninth. This had the overall effect of creating urban centres of concentrated wealth with large sectors of the new proletariat class

Yet it would be incorrect to view this creation of new centres of populace as tantamount to a re-distribution of political power. The political system in Britain ensured that power remained in the hands of the privileged, traditional sectors of society which were still predominantly based in or around London and the South-East. Until the Great Reform Act (1832) rotten boroughs and anachronistic political modelling resulted in the great northern cities such as Leeds, Sheffield and Manchester having only a fraction of the electoral power that their numbers suggested.

But even after 1832 there was no political revolution in England in spite of the continued, and in some areas accelerated, growth of industry and population. Marx and Engels had written their communist manifesto in the 1840’s predicting that the enormous sociological changes that England in particular was experiencing would lead to the birth of Europe’s first truly socialist nation. But there were very few recorded incidents of social unrest as a result of the industrial revolution and examples such as Peterloo (1819) were isolated and meagre in comparison to the widespread class revolutions that the continent witnessed in 1848. “The true explanation is quite simple: wealth. Class conflict was deferred to the twentieth century when international markets and industrial wealth in the North began to contract and working-class standards of living levelled off or actually fell.”

It was not only the physical make-up of England that was shifting as a result of the changes seen since 1780 but also the period saw the birth of an entire sub-nation within the British Isles, namely the people of the industrial heartland of South Wales. Quite simply, without the undoubted industrial revolution, areas such as the Rhondda and Ebbw valleys would remain largely unpopulated today. Rates of urban and social growth in South Wales during the nineteenth century are truly astounding with consequences that the region has yet to come to terms with today.

“The Rhondda demonstrates, albeit to an extreme degree, the nature of the new urban expansion. It was a society of migrants, often far removed from their geographical roots: in 1911, only 58 per cent of the Rhondda’s people had been born in Glamorgan. The rest of Wales supplied 19 per cent, England 7 per cent. A sixth of the population was drawn from ‘elsewhere’, from Ireland and Scotland, but also from Spain, Italy and other lands. The community was disproportionately young and male. Between 1880 and 1914, males generally comprised at least 55 per cent of the population.”

South Wales thus became a frontier nation, completely dependent upon coal for subsistence; it would not exist as we know it today were it not for industrialisation. The example of the new nationality which was borne out of the South Wales coalfields was symptomatic of the broader diffusion of ethnicity that the industrial revolution bequeathed to modern Britain. The influx to British cities of huge numbers of Irish after the potato blight of the 1840’s changed forever the local political, cultural and economic landscape. Along with a large influx of Jews, mostly displaced from Eastern Europe, the immigrants to British cities transformed the fate of the nation; most were willing to perform the worst jobs which enabled grater numbers of the local population to move up the complex industrialised social spectrum. London, in particular, became, during the nineteenth century, a haven for traders, merchants and, increasingly, knowledge with the first university college of London established in 1826. “It was a progressive, enquiring energy which animated all of these concerns. It has been termed the energy of empire since the vast power and resourcefulness of nineteenth century London, at the centre of the imperial world, had somehow managed to infiltrate all aspects of its life.” 

Indeed, it can be argued that the all-encompassing Empire of the latter part of Queen Victoria’s reign could not have occurred without the impetus of the inexorable industrial revolution beforehand. The invention of steam alone necessitated a rail work and domestic infrastructure capable of supporting an empire and, of course, economic imperialism was used much more frequently by the British invaders of India and Africa, as opposed to the militaristic imperialism which characterised the German acquisition of territory after the Franco-Prussian War (1870-1).

Therefore, politically, socially and culturally, Britain was moving forward with great haste without instigating anything remotely close to a revolution in spite of the huge changes already described. Only in terms of economics can this historical period really be seen as fundamentally altering the composition and character of the country, with industrialisation creating the world’s first truly capitalist society. “This was the period when Britain enjoyed to the full the economic benefits of having become ‘the workshop of the world.’ Her total exports in 1850 were worth £71 000 000, in 1870 they were worth nearly £200 000 000. Her imports trebled in those years from £100 000 000 to £300 000 000… whichever way it is looked at, the total wealth of the country was growing fast, and it was more widely distributed throughout the community than before.” The measure of the level of industrialisation ought to be gauged in social and political as well as economic terms. Yet, as contemporary Latin American analysts are discovering, facts and figures pertaining to these phenomena are notoriously difficult to calculate. Economically, however, it is apparent for all to see that the growth of Britain between 1780 and 1914 can only be explained in revolutionary language, as a direct result of an unprecedented industrial revolution.

There is no doubt that the period 1780-1914 was the key timeframe in terms of the British experience of the industrial revolution. The difficulty for historians is the phraseology: revolution implies one key date, a dramatic event and a sudden shift of national focus discernible after that occasion. In comparison to France, for example, British history at this time appears anything but revolutionary – the French experienced three revolutions by the time that the Third Republic was declared passed with the defeat of Napoleon III. Evolution, as opposed to revolution, would therefore be a more accurate term to describe the myriad of changes that beset British society and political life during this period.

And where there did occur a revolution, it took place in factories across the country, in coal fields and the birth of trade unions rather than in the execution or dissolution of monarchy and tradition. Much of the greater social, cultural and political changes that occurred after 1918 were as a result of the groundwork cemented during the period 1780-1914, none greater than the formation of a society based upon class, itself a direct legacy of the industrialisation of the nation, as E.P. Thompson concludes in his own inimitable dissection of the social consequences of the industrial revolution.                              “This collective class consciousness was indeed the great spiritual gain of the Industrial Revolution, against which the disruption of an older and in many ways more humanly comprehensible way of life must be set…the slow, piecemeal accretions of capital accumulation had meant that the preliminaries to the Industrial Revolution stretched backwards for hundreds of years. From Tudor times onwards this artisan culture had grown more complex with each phase of technical and social change.”

BIBLIOGRAPHY

P. Ackroyd, London: the Biography (Chatto & Windus; London, 2000)

P. Clark & P. Slack, English Towns in Transition, 1500-1700 (Oxford University Press; Oxford, London & New York, 1976)

P. Jenkins, A History of Modern Wales, 1536-1990 (Longman; London & New York, 1992)

P. Mantoux, The Industrial Revolution in the Eighteenth Century (Metheun; London, 1961)

P. Mathias, The First Industrial Nation: an Economic History of Britain, 1700-1914: Second Edition (Metheun; London, 1983)

F. Musgrove, The North of England: a History from Roman Times to the Present (Basil Blackwell;  Oxford, 1990)

J. Rule, The Vital Century: England’s Developing Economy, 1714-1815 (Longman; London & New York, 1992)

D. Thompson, England in the Nineteenth Century, 1815-1914 (Penguin; London, 1978)

E.P. Thompson, The Making of the English Working Class (Penguin; London, 1991)

E.A. Wrigley, People, Cities and Wealth (Basil Blackwell; Oxford, 1987)

INDUSTRIAL REVOLUTION

   

HYPERLINK “http://www.timelineindex.com/content/clickout.php?siteid=544” o “Go to Website” t “_blank” http://www.timelineindex.com/content/clickout.php?siteid=544 HYPERLINK “http://www.timelineindex.com/content/search.php?s=+1750” o “Search from year: 1750” 1750 – HYPERLINK “http://www.timelineindex.com/content/search.php?s=+1900” o “Search from year: 1900” 1900 HYPERLINK “http://www.timelineindex.com/content/search.php?s=+1900” o “Search from year: 1900” HYPERLINK “http://www.timelineindex.com/content/select/612” Periods HYPERLINK “http://www.timelineindex.com/content/select/369” Industrial Age HYPERLINK “http://www.timelineindex.com/content/select/1551” 18th Century HYPERLINK “http://www.timelineindex.com/content/select/1552” 19th Century HYPERLINK “javascript:history.go(-1)” o “Previous” Back

  HYPERLINK “javascript:history.go(-1)” o “Previous” INCLUDEPICTURE “http://www.timelineindex.com/imagesThumb/255_91.png” * MERGEFORMATINET   HYPERLINK “http://www.timelineindex.com/content/clickout.php?siteid=544” o “Go to Website: INDUSTRIAL REVOLUTION” t “_blank” INDUSTRIAL REVOLUTION  >  Website  INCLUDEPICTURE “http://www.timelineindex.com/assets/goto.gif” * MERGEFORMATINET The Industrial Revolution was a period of the 18th century marked by social and technological change in which manufacturing began to rely on steam power, fueled primarily by coal, rather than on animal labor, or on water or wind power; and by a shift from artisans who made complete products to factories in which each worker completed a single stage in the manufacturing process. Improvements in transportation encouraged the rapid pace of change. The causes of the Industrial Revolution remain a topic for debate with some historians seeing it as an outgrowth from the social changes of the Enlightenment and the colonial expansion of the 17th century. The Industrial Revolution began in the English Midlands and spread throughout England and into continental Europe and the northern United States in the 19th century.

Cultural Environment of International Business

Cultural Environment of International Business

Name

Institution

Cultural Environment of International Business

Introduction

This article seeks to highlight the various cultural international business elements and the influence they have on international business cultural diversifications mainly the manners, language, attitudes and values. With the progression of globalization its effects on global business activities are more evident, in the drastically evolving world of economic globalization and on this aspect the urgency and importance of cross-cultural negotiations in international business is heightened. It is common knowledge that each country exhibits a unique culture, and this makes cultural barriers and communication an issue in business communication, since it can easily influence the international bargaining decisions. This can be viewed from the aspect of values existing in groups that have similar norms and beliefs and it is from these same values that they base their attitudes.

It is with the above understanding that the unique cultural standards are the main factors that affect the decisions made, strategies implemented, and way of thinking, which if enforced correctly can address the international business cultural conflicts while coordinating the right attitudes in the international business that can facilitate adaptation to the new culture and avoid any unnecessary miscommunication or misunderstanding.

The initial selection of the Canada Timber team can be said to have been selected based on the cultural attributes of the Canadian country, which could be reviewed by using Hofstede analysis and this made it to be a mistake on the company since it was bias. These attributes include the individualistic and self-reliant nature of the Canadian society which often portrayed as having loose bonds as seen with the CEO when he chose his brother in law to be the company representative, mainly since he had close family relations instead of someone who would have been more knowledgeable on the Japanese culture (Sarah Mady, 2013).

The regional sales person was also wrongly chosen since the CEO knew he married a Japanese but the only reason for taking him along was for boosting his image even though he knew the person had limited grasp of both the language and the culture in that country. It can also be said that he mainly chose the specific management and production team members to accompany him due to their wide knowledge on the topics and their success which reflected the aspect of the Canadian society that uses personal achievement to measure success, while also demonstrating the low (PDI) power distance in the company. The choice the CEO made would have been appropriate if he included an agent or collaborator who had vast experience in dealing with foreign cultures and through that they would have been able to overcome the various obstacles on communication that were relayed through the nonverbal means like the body language, gestures ,eye-contact and facial expressions.

The main differences in the Canadian and the Japanese culture include things like in the Japanese culture the meetings are mainly held for exchanging information, building a rapport, or confirming on the decisions that had been made previously, this is in contrast to the Canadian culture where the meetings are mainly for finishing and signing on agreements like in contracts or projects. The Japanese culture utilizes the first meeting to access the individuals’ suitability in terms of doing business, which contrasts with the Canadian culture that ascertains an individual capability by analyzing previous success. The Japanese culture allows for implicit communication which is mainly revealing of less information and leaving the other person to fill in the rest, while the Canadian culture allows for practice of explicit which is direct opposite to the latter. The Canadian culture does not support routine giving of gifts, which it has reserved for celebrations example on finalizing a contract deal, but in the Japanese culture gift giving is a common tradition, they also value things like exchanging of business card which they regard as signs of respect to the individual and honor it with celebration, unlike in the Canadian culture that does not place any value on card exchanging.

The Japanese culture is more accommodative and flexible compared to the Canadian. The Japanese culture is more reserved and they demonstrate this by their well calculated expressions of emotions and choice of words, as compared to the Canadian which tends to support a more free expression of thoughts and feelings as exhibited by the favored expression of moods on the faces mainly, happiness, joy or exhaustion. The nature of development culture in Japan also differ since it is mainly based on long or high term basis, as compared to the low or short term basis of the Canadian culture.

The things that should have been done differently include the management understanding what the foreign business partners considered as normal in their country, which is of relevance and needs careful evaluation and critical thinking since, it encompasses a holistic view that includes relationships, time, communication, and human condition. In addition the management could have hired a professional agent who could have taught them the basic different cultural aspects they were likely to encounter as a way of reducing the culture shock and the misunderstanding that occurred, the selection of the team to travel would have had a more wider criteria rather than the one led by feelings. The management should have also done some research to find out the perception the foreigners had about their culture, and through understanding those aspects of the cross-culture they would have been aware of the general business environment, ethics, regulations, and negotiations that were available (Vern Terpstra, et, al 1987).

Exercising more patience and trying to understand the cause of the sudden silence instead of panicking, pushing for the contract closure and constantly reducing the initial price, as the CEO did these rash decisions made him loose credibility and eventually the contract according to the Japanese culture since the culture distrusts an inconsistent person. Instead I would have refocused the emphasis to retaining the harmony in the context of the Japanese culture in forms that would adequately allow many forms of vague expressions and the cultural relevance behind this implementation would be that by avoiding explicit or direct statements there was a better chance of not causing any offense rather than if let alone.

In conclusion competition success and communication has been known to be influenced by cultural factors and it is with this that cultural awareness helps in the shaping of the behavior of a firm in international markets that have a reflection of cross-culture tendencies. The broad recognition that cultural factors often hinder global business communication and the fact that a firm can understand the various cultural differences and implement the right skills to address the issues is one of the key strategies they can implement in order to have a competitive edge in global business.it is with this understanding that economic growth can better be explained by culture as compared to material changes or structure

The acceptance of valuing perseverance, thrift and hierarchy legitimacy without undue emphasis on social and traditional obligations could impede the initiatives of business, competitive tendencies that disregard cultural harmony, values and individualistic tendencies all have changing and pervasive influences on the global markets and due to this markets often have to either adopt or change to address the change.

Reference

Sarah Mady (2013) Cultural Environment of International Business, How CULTURE works, KOGOD School of Business American University, Washington, DC

Vern Terpstra and Kenneth David. (1987)The Cultural Environment of International Business, Printed in the United States of America by SOUTH-WESTERN PUBLSHING CO. Cincinnati, Ohio.