Numerical Methods to solve equations Essay Example for Free

Numerical Methods to solve equations Essay The table above shows the numbers of iterations each method took in order to come to the same degree of accuracy. The Newton-Raphson method was the quickest, finding the root within a certain degree of accuracy in only three iterations. Second was the Decimal Search, which took five iterations and last was the Rearrangement Method, which took the most number of iterations, 6. Newton-Raphson method is clearly the fastest and the most efficient method to use as the number of iterations needed to find a root to a degree of accuracy is small. However, this method is very tiresome to calculate by hand and the tiniest mistake can result in a wrong answer. The Decimal Search takes more iteration; but, this method is the easiest and easily understood. However, this method is best done on a spreadsheet, where you would be able to spot the sign change easily. The Rearrangement Method takes slightly more iteration but it provides the root to any degree of accuracy. Also, the formula is iterative, therefore, it is not very time consuming. However, finding can be tricky. In terms of the software used, Decimal Search was the easiest as it only required spreadsheet which is not difficult to use. Although making the tables can be repetitive, any faults can easily be rectified. Both the Newton-Raphson Method and the Rearrangement Method used a calculator to work out the iterative steps. This was often very time-consuming and frustrating as simple mistakes could let to the wrong route. Autograph was used to draw all the graphs and show the methods at work. It was not hard to use but tricky, due to the different options available.

Wolves Essay -- essays research papers

Wolves The wolf was once a much slandered animal. In the western world, people feared and hated wolves, and this legacy is reflected in stories such as Little Red Riding Hood and The Boy Who Cried Wolf. In these popular children's tales the wolf is made out to be a prowler and a killer of livestock and people. There is some basis for The Boy Who Cried Wolf, for wolves have killed cattle and sheep. But what of Little Red Riding Hood? There are no records of wolves killing humans in Canada or the United States. Yet, when wolves were spotted near rural communities, fear used to grip the populace, but over time this has become less prevalent. Today, many people know that scientists studying wolves have lived very close to dens where there were pups without being attacked. They have even taken pups from a den without being injured. The parents have usually run away, returning later to take their young to a more private den or to a rendezvous site (a place where the pack meets). In areas where wolves are hunted or trapped they fear people and are very wary. However, in remote places, such as in the Canadian Arctic, they show little fear and will often allow people to live near them. Two hundred years ago, Canis lupus, also known as gray wolves, were more widely distributed than any other mammal of historic times. They lived in large areas of North America, Europe, and Asia; the only places they could not occupy were deserts, tropical rain forests, and peaks of the highest mountain ranges. Wolves still live in large areas of the northern hemisphere; however, their primitive range has been greatly reduced due to changes in the landscape and people's efforts to exterminate them. In North America, wolves have been exterminated in the Atlantic provinces, Mexico, the United States (except Minnesota, Alaska, and some of the western states), and the heavily populated areas of southern Canada. They are still common in lightly settled portions of Canada from Labrador to British Columbia and in the Yukon and Northwest Territories. The red wolf was once common in the southeastern United States. It has been eliminated in the wild. However, through a captive breeding program, the species is being reintroduced into its former range. It is virtually impossible to describe the typical appearance of wolves. Wolves of many large arctic islands and Greenland usually appear sn... ...ibou numbers decline. Wolves have already been exterminated in many places. However, there may be less danger of such excesses in the future, as wolf control is increasingly based on biology rather than emotion. There is now a greater awareness among people that the killing by wolves of deer and other prey species, which we may want for ourselves, is not a sufficient reason for the extermination of wolves. Sometimes populations of game animals are critically low, so on biological grounds wolf control could be justified; however, control programs are always opposed by ever-increasing urban populations. Proposed wolf culls have become major political issues in many areas in North America. When controls are carried out, they need to be done to meet certain criteria, which are based on sound scientific information and stewardship of wildlife populations. In the wilderness scheme of things wolves play an important role. And from a human point of view, the great interest and value of having this intelligent animal as part of our wilderness heritage should be sufficient justification for allowing it to survive in a wide variety of wilderness and semi-wilderness areas all over the world.

Rising Petrol Prices

Rising petrol prices 1) When and how did the cost of petrol start to rise? 2) Are there anybody else who is involved other than the drivers of motor vehicles? 3) Can we overcome the rising costs of petrol 4) Are there any advantages of the rising of petrol costs at all 5) How does the rising costs of petrol affect the Demand, Supply, Employment and Income section of the cycle Petrol prices have been continually soaring throughout the decades with GST (goods and service tax), the level of demand, the gulf war and the fact that we are running out of it being the main factors. In some cases the level and extent of competition of petrol companies in a particular location may also be a factor. Motor Vehicle drivers aren’t the only ones who’s suffering from expensive petrol, Aviation companies are also effected, recent surveys have shown that 28% of aviation companies prefer going for a more direct routing to their destinations, 40% found flying at slower speeds to save petrol, 19% cut back on hours flown, 15% started tankering fuel (getting it while it is at a lower price to save money). We certainly cannot overcome the rising of petrol prices but people in Australia and around the world are trying to help by changing their driving habits, using public transport more often and coming up new ways to make cars more fuel efficient. It is quite obvious what the disadvantages are when it comes to talking about the rising costs of petrol but when it comes to advantages I think that people are starting to cut back on shopping sprees, dinner dates and night outs because they want to save money and use it for petrol. There are also fewer teens on the roads because most of them obviously can’t afford petrol when the prices are this high which means that there are less drunk road accidents. A lot of people are also losing weight as a result of using bicycles to save petrol. ———————– A lot of people in the world want oil all at the same time. Oil reserves are running low on Fuel. (Oil supply do not meet demand expectations) They do not make as much money Employment stays the same DEMAND (goes up) Supply Employment Income

Can a National Sales Tax Replace Income Taxes in the U.S.

Tax time is never a pleasant experience for any American. Collectively, millions and millions of hours are spent filling out forms and trying to decipher arcane instructions and tax regulations. By filling out these forms and perhaps even sending an additional check to the Internal Revenue Service (IRS), we become painfully aware of how much money we actually put into federal coffers each year. This heightened awareness generally causes a flood of proposals on how to improve the way governments collect funds. The Fair Tax Act of 2003 was one such proposal. The Fair Tax Act of 2003 Back in 2003, a group known as Americans for Fair Taxation proposed replacing the United States income tax system with a national sales tax. Representative John Linder of Georgia even went as far as to sponsor a bill known as the the Fair Tax Act of 2003, which ended with fifty-four other co-sponsors.  The acts stated aim was to: â€Å"To promote freedom, fairness and economic opportunity by repealing the income tax and other taxes, abolishing the Internal Revenue Service, and enacting a national sales tax to be administered primarily by the states. A fellow About.com expert, Robert Longley, wrote an interesting summary of the Fair Tax proposal  that is worth checking out. Though the Fair Tax Act of 2003 ultimately did not pass, the questions raised by its presentation and the underlying concepts of the move from an income tax to a national sales tax still remain a highly discussed topic in the economic and political arenas. Proposal for a National Sales Tax The core idea of the Fair Tax Act of 2003, the idea to replace the income tax with a sales tax, is not a new one. Federal sales taxes are widely used in other countries around the world, and given the low tax burden compared to Canada and Europe, it is at least plausible that the federal government could obtain enough revenue from a sales tax in order to completely replace federal income taxes. The Fair Tax movement represented by the 2003 act proposed a scheme in which the Internal Revenue Code would be amended to repeal subtitle A, subtitle B, and subtitle C, or income, estate and gift, and employment taxes respectively. The proposal called for these three areas of the tax code to be revoked in favor of  a 23% national sales tax. It is not difficult to see the appeal of such a system. Since all taxes would be collected by businesses, there would be no need for private citizens to fill out tax forms. We could abolish the IRS! And most states already collect sales taxes, so a federal sales tax could be collected by the states, thus reducing administrative costs. There are a lot of apparent benefits to such a change. But in order to properly analyze such a large change to the American tax system, there are three questions we must ask : What impact will the change have on consumer spending and the economy?Who wins and who loses under a national sales tax?Is such a scheme even feasible? We will examine each question over the next four sections. One of the largest effects a move  to a national sales tax system would have is to change peoples working and  consumption behavior. People respond to incentives, and tax policies change the incentives people have to work and to consume. It is unclear if replacing an income tax with a sales tax would cause consumption within the United States to rise or fall. There will be two primary and opposing forces at play: 1. The Effect on Income Because income would no longer be taxed under a national sales tax system like FairTax, the incentives to work would change. One consideration would be the impact on a workers approach to overtime hours. Many workers can choose the amount of overtime they work. Take, for example, someone who would make an extra $25 if he worked an hour of overtime. If his marginal income tax rate for that extra hour of work is 40% under our current income tax code, he would only take home $15 out of the $25 as $10 would go toward his income taxes. If income taxes are eliminated, he would get to keep the whole $25. If an hour of free time is worth $20, then he would work the extra hour under the sales tax plan, but not work it under the income tax plan. So a change to a national sales tax plan reduces the disincentives to work, and workers as a whole would likely end up working and earning more. Many economists argue that when workers earn more, theyll also spend more. So the effect on income suggests that the FairTax plan could cause consumption to increase. 2. Changes in Spending Patterns It goes without saying that people dont like paying taxes if they dont have to. If there is a large sales tax on purchasing goods, we should expect people to spend less money on those goods. This could be accomplished in several ways: Spending less and saving more. Of course, todays savings are likely to be used for tomorrows consumption, so consumers may just be delaying the inevitable. But workers may still wish to save more now as opposed to spend, as they may believe the sales tax will not last forever or they may plan on finding other ways to avoid the tax in the future.Spending money outside of the United States. Currently if consumers wish to spend their money cross-border shopping in Canada or on a vacation in the Caribbean, they have already been taxed by the Federal government on that money at the income level. Under a sales tax scheme, they can spend their earnings outside the country and not be taxed on any of it, unless they bring enough goods back into the United States. So we should expect to see more money spent on vacations and outside of the United States, and less money spent domestically within the United States.Spending in a manner that evades taxes. If there is an easy way to evade taxes, it is highly likely that a large number of people will exploit it. One way to evade a national sales tax would be to claim your spending as a business expense, even if it is a purchase for personal use. Goods which are used in production, known as intermediate goods, are generally not subject to a regular sales tax. The government could close this loophole by making the sales tax a Value Added Tax (VAT) like the Canadian Goods and Services Tax (GST). But VATs and GSTs are rather unpopular with the business community, as they raise the costs of production, so it is unlikely the U.S. would want to embark on this path. With a high sales tax rate, tax evasion will be prevalent, so this effect will cause a decrease in spending on taxed goods. Overall, it is not clear whether consumer spending would increase or decrease. But there are still conclusions we can draw on what effect this will have on different parts of the economy. We saw in the previous section that a simple analysis cannot help us determine what would happen to consumer spending were a national sales tax system like the one proposed by the FairTax movement be implemented in the United States. From that analysis, however, we can see that a change to a national sales tax is likely to influence the following macroeconomic variables: Production would likely rise as marginal income tax rates fall to zero, which induces people to work extra hours.Take home income would rise as people are not taxed on income and presumably may work extra hours.Consumer spending within the United States may or may not rise.Saving and spending abroad would likely increase, which would cause:A weakening of the U.S. dollar as Americans who want to buy foreign goods will need to exchange their U.S. dollars for foreign currency. We should expect to see the U.S. dollar become less valuable relative to other currencies, particularly the Canadian dollar.The price of investment goods such as bonds may rise as people wish to save more, so interest rates would fall.The after-tax price of consumer goods would go up due to the new sales tax. The pre-tax price of consumer goods, on the other hand, would be more likely to fall since increased productivity would cause an increase in the supply of goods. We have seen that we cannot be sure whether or not there would be an increase or decrease in demand for consumer goods purchased within the United States. The price of these consumer goods would increase, but not by the full amount caused by the tax increase.The price of goods outside of the United States (particularly in Canada) would likely increase because of this increased demand. Cities such as Windsor, Ontario should expect to see even more American visitors than they do already. It is important to note, however, that not all consumers would be affected equally by these changes. Well next look at who will lose and who will win under a national sales tax. Changes in government policy never affects everybody equally and not all consumers would be affected equally by these changes. Lets take a look at who would win under a national sales tax system and who would lose. Americans for Fair Taxation estimates that the typical American family will be over 10% better off than they currently are under the income tax system. But even if you were to share the same sentiment as Americans for Fair Taxation, it is clear that all individuals and American households are typical, so some would benefit more than others and, of course, some would benefit less. Who Might Lose Under a National Sales Tax? Seniors. People do not earn income at a steady rate during their lifetime. The bulk of most peoples earnings occurs before the age of 65. People over the age of 65 have vastly reduced incomes and typically live off the savings they earned while employed in addition to programs like Social Security. A switch to a national sales tax would, in effect, result in taxing much of that money twice. These individuals would have already paid a lifetime of income taxes and would now be living off of a mix of previously taxed and tax-deferred savings. Under a new national sales tax system, the previously taxed savings would essentially be subject to tax again when used for purchases. Unless special consideration is given to the current generation of seniors, they would end up paying a disproportionate share of taxes. The Poor. Generally under the current system, the working poor pay very little (if any) income tax. But everyone needs to consume to survive. The poor would get hit twice under suc h a scheme. While currently the poor pay very little tax, under the new system they would have to pay taxes on their consumption, so their total tax bill would rise dramatically. The poor also spend a larger proportion of their total income on consumption goods to survive, so they would ultimately pay a larger percentage of their income in taxes than wealthier individuals. The FairTax advocates realize this, so their plan includes sending each American family a rebate or pre-bate check each month to cover the necessities of life. The size of the checks would be designed such that a family right at the poverty line would not pay a cent in taxes. Of course, the higher the allowance made for the poor, the higher the tax rate everyone else will pay in order to cover federal spending.Economist William G. Gale at the Brookings Institute has determined that most low income families would still pay more taxes under a national sales tax system, stating, Under the Americans for Fair Taxation proposal, taxes would rise for households in the bottom 90 percent of the income distribution, while households in the top 1 percent would receive an average tax cut of over $75,000. Families.  The current American income tax offers all sorts of deductions for small families such as earned income credits and child care credits. Under a national sales tax system, these would disappear with the elimination of the income tax. A sales tax, other than for purposes of the rebate, would not distinguish between families and individuals. Gale states that the enactment of a broad-based, flat-rate consumption tax like the sales tax ... would hurt families with incomes less than $200,000, because of the loss of tax preferences, but would help families with income above $200,000, due to the dramatic reduction in the top tax rate. Given that the rebates in the current proposal would be given based on proximity to the poverty line, this is not surprising. IRS Employees and Income Tax Lawyers. Pa rt of the appeal of the proposal is that it will make the IRS irrelevant, which would eliminate the need for jobs in these industries, while likely not creating enough or any new opportunities for these displaced workers. Having looked at those groups who would likely lose under a national sales tax system such as the one proposed by the FairTax movement, we will now examine those who would benefit most. Who Might Win Under a National Sales Tax? People who are inclined to save. A consumption tax can be avoided by not consuming. So it makes sense that people who do not consume a lot will benefit from the plan. Gale admits that there are savings for a large portion of the population, stating that if households are classified by consumption level, a somewhat different pattern emerges. Households in the bottom two-thirds of the distribution would pay less than [they do] currently, [while] households in the top third would pay more. Still households at the very top would pay much less, again receiving a tax cut of about $75,000.People who can shop in other countries.  This group includes people who take a lot of  overseas vacations and Americans living near either the Canadian or Mexican border who can do their shopping in those countries to avoid American sales taxes.People who own businesses.  The sales tax will only be charged on goods bought by individuals, not by firms. Owning a business would give an individual an adv antage as goods could be purchased free of sales tax if they are claimed as business expenses.The wealthiest one percent.  As stated previously, this group would likely see an average tax cut of $75,000 per person. National Sales Tax Conclusions Like the flat tax proposal before it, FairTax was an interesting proposal to solve the issues of an overly complex system. While implementation of a FairTax system would have several positive (and a few negative) consequences for the economy, groups that lose under the system would certainly make their opposition known and those concerns would need to be addressed explicitly. Despite the fact that the 2003 act did not pass in Congress, the underlying concept remains an interesting idea worth discussing.