Exponential Decay Definition and Function

In mathematics, exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. It can be expressed by the formula ya(1-b)x  wherein y is the final amount, a is the original amount, b is the decay factor, and x is the amount of time that has passed. The exponential decay formula is useful in a variety of real world applications, most notably for tracking inventory thats used regularly in the same quantity (like food for a school cafeteria) and it is especially useful in its ability to quickly assess the long-term cost of use of a product over time. Exponential decay is different from  linear  decay  in that the decay factor relies on a percentage of the original amount, which means the actual number the original amount might be reduced by will change over time whereas a linear function decreases the original number by the same amount every time. It is also the opposite of exponential growth, which typically occurs in the stock markets wherein a companys worth will grow exponentially over time before reaching a plateau. You can compare and contrast the differences between  exponential growth and decay, but its pretty straightforward: one increases the original amount and the other decreases it. Elements of an Exponential  Decay Formula To start, its important to recognize the exponential decay formula and be able to identify each of its elements: y a (1-b)x In order to properly understand the utility of the decay formula, it is important to understand how each of the factors is defined, beginning with the phrase decay factor—represented by the letter b  in the exponential decay formula—which is a percentage  by which the original amount will decline each time. The original amount here—represented by the letter a  in the formula—is the amount before the decay occurs, so if youre thinking about this in a practical sense, the original amount would be the amount of apples a bakery buys and the exponential factor would be the percentage of apples used each hour to make pies. The exponent, which in the case of exponential decay is always time and expressed by the letter x, represents how often the decay occurs and is usually expressed in seconds, minutes, hours, days, or years. An Example of Exponential Decay Use the following example to help understand the concept of exponential decay in a real-world scenario: On Monday, Ledwith’s Cafeteria serves 5,000 customers, but on Tuesday morning, the local news reports that the restaurant fails health inspection and has—yikes!—violations related to pest control. Tuesday, the cafeteria serves 2,500 customers. Wednesday, the cafeteria serves only 1,250 customers. Thursday, the cafeteria serves a measly 625 customers. As you can see, the number of customers declined by 50 percent  every day. This type of decline differs from a linear function. In a linear function, the number of customers would decline by the same amount every day. The original amount (a) would be 5,000, the decay factor (b ) would, therefore, be .5 (50 percent written as a decimal), and the value of time (x) would be determined by how many days  Ã¢â‚¬â€¹Ledwith wants to predict the results for. If Ledwith were to ask about how many customers he would lose in five days if the trend continued, his accountant could find the solution by plugging all of the above numbers into the exponential decay formula to get the following: ​ y 5000(1-.5)5 The solution comes out to 312 and a half, but since you cant have a half customer, the accountant would round the number up to 313 and be able to say that in five days, Ledwith could expect to lose another 313 customers!

The Kings Great Matter Essay - 1699 Words

The Kings Great Matter The Spanish-English marriage alliance of Catherine of Aragon and Prince Arthur was arranged when the children were very young. Catherine traveled to England only to face tragedy when her young husband, Arthur died in 1502.Henry VII wanted to marry Catherine to his younger son, who would be, Henry VIII so that he did not lose the dowry money from Catherines parents and to secure some other agreements between the two countries. In the Catholic Church, it was forbidden to marry the wife of a deceased brother. A papal dispensation was required for the marriage. It was easily obtained from Pope Julius II. Henry VII died before the marriage took place but Henry VIII immediately married Catherine once he became†¦show more content†¦Throughout this time period, Cardinal Wolsey, an advisor to Henry and very powerful in the Catholic Church, moved closer and closer to Henry. As the relationship progressed Henry became more distant to Catherine. Wolsey spied on Catherine and she thought he acted against her always. She began to believe that Wolsey had always hated her and possibly that she had always hated him also. She held him responsible for the promotion of Henrys bastard son, for tempting the King of France to break the word agreed at Madrid and plunging Europe into war, for ruining the alliance between the two countries, and for seducing the pope and the Italian states. She also held Wolsey responsible for Henrys irritability. It isnt surprising that Catherine also blamed Wolsey for Henry wanting to divorce her. But, Catherine was not the only one with this idea. The ambassador, the emperor, Reginald Pole, Catholic controversialists, and Catholic writers ever since have agreed that Wolsey was probably the instigator. Catherines thought that Wolsey had put the ideas of divorce into Henrys head was very reasonable. She believed that Wolsey thought this was the best way to safeguard his pro-French policy by removing Catherine and replacing her with a French princess. Wolsey was serious about his French alliance and did hope to arrange a French marriage. He also feared Catherine. He knew that he needed to get rid of her so that he get closer to the king and help him handle hisShow MoreRelatedA Rhetorical Analysis: of I Have a Dream Essay1484 Words   |  6 PagesIn Martin Luther King’s I Have a Dream speech, King makes use of an innumerable amount of rhetorical devices that augment the overall understa nding and flow of the speech. King makes the audience feel an immense amount of emotion due to the outstanding use of pathos in his speech. King also generates a vast use of rhetorical devices including allusion, anaphora, and antithesis. The way that King conducted his speech adds to the comprehension and gives the effect that he wants to rise above the injusticesRead MoreStory from Haitian People, Inside the Kings Bull by Essay583 Words   |  3 PagesIn the story of Bouqui and Malice â€Å"Inside the King’s Bull† is a very old story that the Haiti people have been telling their kids for hundreds of years. From a western perspective this story is very bizarre for the simple reason it doesn’t follow any western logic when it comes to the moral of the stories. To make matters worse most westerners have no idea of who is Bouqui or Malice; even though, their stories have been around for such a long time. Not only do westerners have no idea, but many historiansRe ad MoreEssay on The Kings Dream1588 Words   |  7 Pagesaddressed a speech that he had written and spoke of it at the Lincoln memorial in Washington D.C on August 28, 1963. 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Internet Banking in India free essay sample

The banking sector in India has undergone a rapid transformation. Almost a decade ago this area was limited to nationalized banks and cooperative. Then came the multinational banks, but were these limited to serve small elite.  One could consider the past as the Middle Ages in the banking sector, in which each branch of the same bank acted as independent information silo and multichannel banking (ATMs, Net Banking, tele-banking, etc) was almost nonexistent. The main reason for this first transformation is due to improved methods developed encryption security and Internet. The second reason is that banks do not want to lose a potential market share for banks that are quick to offer their Internet services. The objective of this research is just comparing the modern era banking system with the old one. The evolution of modern banking technology began with the use of advanced machines shipping Ledger (ALPM) in the 1980s. The Reserve Bank of India, which is a central policy under which several public sector banks, financial institutions, NBFCs etc. working in India had advised then all banks to go massive computerization branch level. Two options were raised i. e. either to automate the front office or office. Many banks opted for ALPM office automation in the first phase. Banks as State Bank of India, a public sector commercial bank, focused on automating back office in branch level. The Rangarajan Committee 1985 report said the banks had to get computerized. The second wave of development called for Total Bank Automation (TBA) in late 1980. This automated both the front-end and back-end operations within the same branch. TBA compound total automation of a particular branch with its own database. In the third wave, the new private sector banks entered the field. These banks have opted for a different model of having one central database instead of having multiple databases for all branches. This was possible thanks to the availability of good network infrastructure. In the beginning of the 1990s, the cost of the leased line goes down. The DoT was expanding its capacity and new technologies were being implemented. Earlier, banks were unsure of directing the whole operation through a single data center. However, when a couple of private sector banks implemented efficiently, other banks began to show interest, and also began consolidating their databases in a single database [8]. Banks follow this movement by choosing appropriate application software that supports centralized operations. The fourth wave began with the evolution of ATM delivery channel. This was the first stage of training the client for their own transactions. The second stage was Suvidha experiment in the city of Bangalore in India. This showed the power of technology and how the scope can be increased at a rate unusually large. Seeing this, all banks began to renew their retail distribution channels. Their main focus became the number of customers they can service at a lower cost. The main channels are chains such as Internet banking and mobile banking. After this came alliances for payment through different gateways. The third major event happening now is the real time gross settlement system of the RBI. Once this is in place, transactions between banks can be done through the settlement system, online, electronically. So collections will become very fast. Within five years, most transactional services are provided by way of the Internet. Net-based banking takes only 10 percent of the operating costs of conventional banking practices and services. Because banks will play a key role in terms of public services related to electronic money transactions we feel that cooperative banks NET-Banking should consider in a big way. A cost comparison study by IBM Global Services Consulting Group clearly shows the advantage of using Internet for banking services through another Traditional media. The opening of the Indian banking sector to private players acted as a turning point for the transformation. De-regulation efforts led many financial institutions (such as HDFC and ICICI) and non-financial institutions entering the field of banking. With the entry of private players in retail banking and with multinationals focuses on individual consumers in a big way, the banking system experienced a change a phenomenal. Multi-channel banking gained importance. For the first time consumers have the option conducting transactions in either the traditional way (through the bank branch), through ATMs, by phone or through the network. Technology played a key role in providing this multi-platform service. Input private actors driven patterns combined with new nationalized banks forced to redefine their core banking strategy. And technology is central to this change. Internet Banking is the most effective means of banking. The bank customers changing relationships significantly, open standards replace property front ends, many-to-many substitution networks single line, links and traditional locking erosion, so that corporations enjoy lower switching costs. Corporations source worldwide and find the best cane. Corporate customers are free to disaggregate their corporate banking shopping, selecting the best genetics for every need, geographic and functionally, and the integrated use of front-end to manage the complexity of multiple vendors. Methodology: Let us now compare the IT journey of two of the leading banks of india i. e. Pnb and hdfc. Punjab National Bank Punjab National Bank (PNB), a public sector commercial bank, has come a long way since March 2000, when IT systems are deployed only 500-odd branches, and was very uneven. Only 35 percent of the bank business was computerized and a number of small software packages running on independent PCs. Now 2003, GNP had 101 branches in a WAN, deployed core banking infrastructure and network works 175 ATMs. It has also deployed a reliable security infrastructure that helps make transactions within its carefree branches. The journey does not end here, but along the way banks gathered valuable knowledge and experience. Some of the preconditions were that the RBI systems must be audited by an independent auditor, and an independent agency should carry authentic out penetration tests. The bank has already had their systems audited by an external agency, and penetration testing process is ongoing. In the process, GNP has developed the skills of its own staff to take charge of security on their own at a later stage. The bank also hire technically trained personnel to provide the necessary knowledge base. With the launch of Internet banking, the bank will also strengthen its security policies. A private sector bank had a centralized IP-based network right from its inception. All branches throughout the country converge at their respective location zonal center, which in turn connects to the data center Mumbai. Based on the nature of the entity and spoke network architecture, the branches are distributed in different regions and each position has an important regional center. Falling branches under a location connected to the hub in the main area. These hubs then connect to the central site (data center) using a combination of 2 Mbps tubes and 64 Kbps, depending on the total volume of transactions passing through. A highlight of HDFC Bank Network is the presence of two or more hubs in one place. Pre-Internet banking A security issue during the pre-Internet has more to do with the internal activities of a company. From the early days as technology solutions for banking applications mainframe, AS400 or Unix- had a lot of security built. Transactions that are directed from the branch to the main server is encrypted no individual passwords and many functions have two levels of authorization. Therefore safety banking largely integrated in the software or the application itself. Today banking in India is not limited to a branch. People have less time to devote to their banking and would like to make use of banking services through other channels. In a competitive market, where services offered command market share, banks are constantly competing for customers. Banking has become a process of choice and convenience. By offering different channels until banks have succeeded in divert their operations from one branch to other channels. The result has been a reduction in the cost per transaction at the branch. An average transaction costs about 100 rupees branch, at an ATM in question Rs. 0, and the Internet is around Rs. 20. But unfortunately a very small percentage of customers out not use the Internet Banking in India. This is due to factors such as low PC penetration, and penetration of Internet itself is low. At present only a few banks (eg HDFC, PNB, etc) have demonstrated the Internet initiative banking and have a strong advantage over other banks through a large number of customers still use ATMs. Typically 55 percent, on average, the operations of these banks are in the ATM, branch 30 percent, 8 percent Phone and 7 percent Internet. As with any new technology issue new face. There are a number of problems faced by these banks. One of the first problems is that of customer service. Banks need to create a whole new customer relations department to help customers. Banks need to ensure that customers receive help quickly if they need help. The major problems or disasters can destroy banks reputation quickly and easily. By showing the customer that the Internet is reliable they are able get the client can trust the online banking more and more. Besides these the first is the main concern of the laws. While Internet banking has no national or state borders, the law does. Companies will have to make sure you have the software in place that can detect when a law of a state to another is being violated. Security of course, is a big problem with banks. Along with security problems and manage cryptographic a bank also has to worry about becoming a far too cold for the customer. Some think the banks offering Internet banking services our increasingly cold and impersonal with customer. Despite the problems that exist however, are not as bad as you think. With encryption and security technology to improve in leaps and with banks and financial institutions are allowed to use 128-bit Internet banking is increasingly Code secure. The future of modern banking integration is, as people have less time for banking. My profile revealed that the banks that offer online banking services are rapidly becoming the choice of citizens in the urban areas. People want to process more transactions online. Soon there will be more activity in terms of applications and services on mobile. Geography is not an inhibitor more, since all can run on the network. Integration will become the next big thing in real. The customer will want a one-stop workshop that will take care of all your needs. For example people will want to buy their mutual funds, redeem his mutual funds, insurance policies buy, renew policies, and buy movie tickets, train tickets and numerous similar transactions through the bank. The ATM still serve as an effective means of dispensing, but the Internet and mobile will be very active. Banks that use the Internet banking have higher rates of return deposits and provide higher interest rates in general, and not have to deal with cashiers, branches, etc. and then in the times ahead and the actual Virtual banks will not dominate the future.

Summary On The Raven Essays - Poetry By Edgar Allan Poe,

Summary On The Raven Edger Allen Poe's poems are best known for their haunting themes. For example in the poem ?The Raven? which was published in 1845 seemed to be filled with melancholy and thoughts of death. Poe makes use of symbolism in the poem ?The Raven?. On line 3 Poe writes, ?While I nodded, nearly napping, suddenly there comes a tapping?, I think that's a sign that this entire poem takes place while he is in the state of unconscious (dreaming). Again on lines 37 & 38 he writes, ?Open here I flung the shutter, when, with many a flirt and flutter, In there stepped a stately raven of the saintly days of yore?, I believe that the raven symbolizes some after life figure. On lines 81,82 S Poe cries, ?Wretch, ?I cried, ?thy god hath lent thee- by these angels he hath sent thee Respite- respite and nepenthe, from thy memories of Lenore!? Quoth the Raven, ?Nevermore?, here it is clear that the Raven who reiterates, Nevermore, in Poe's dream has been sent to help him relinquish his thoughts of Lenore.