Minireview of A Study Essay Example for Free

Minireview of A Study Essay Synaptic transmission in vertebrate neuromuscular junctions forms the basis of this study. The communication between neurons in the nervous system occurs largely due to neurotransmitter release at the synapses. Messages on the various significant nervous system functions are coordinated through the synaptic junctions and the release of neurotransmitters. Ryanodine receptors are found in the somata of the Purkinje cells, basket cells and pre-synaptic terminals of specific synapses and terminals of basket cells. Calcium in the extracellular fluid triggers the neurotransmitter release. Now it is understood that pre-synaptic stores could participate in this same function. Ryanodine-sensitive stores of calcium also play a role. The quantum is the amount of spontaneous signals occurring in the absence of pre-synaptic action potentials and is equivalent to the release of one neurotransmitter vesicle (Katz, 1969). The action potentials are called miniature currents. For central synapses in the brain, large miniature currents are believed to arise from the release of many neurotransmitter or presynaptic vesicles and in the range of several quanta (Bekkers, 1994). Yoshida’s study (1994) revealed that these multivesicular miniature events could actually be tetrodotoxin-resistant action potentials in the pre-synaptic terminals. Other researchers have tried to explain the phenomenon from another angle, using the presence of intracellular calcium stores in the pre-synaptic terminals. Nakanishi et al localized inositol triphosphate receptors in the neural tissue of the developing and adult mouse brain (1991). These were immunolocalised in the pre-synaptic terminals of the deep cerebellar nuclei and the retina of the eyes. Narita’s studies (1998, 2000) revealed the action of ryanodine-sensitive calcium stores at the frog neuromuscular junctions. It was discovered that agents which influence the ryanodine-sensitive Calcium stores also increased the intracellular Calcium in the pre-synaptic cells and regulated acetyl choline release during high frequency stimulation. Mothet et al (1998) studied the action potentials at the pre-synaptic terminals of the buccal ganglia in Aplysia. They indicated that ryanodine inhibited while the pre-synaptic injection of Cyclic ADP Ribose augmented the action potential evoked release of acetyl choline at synapses. Studies also showed that caffeine with or without ryanodine modifies Calcium stores at the pre-synaptic terminals in autonomic ganglia (Peng, 1996; Smith et al, 1996) and in photoreceptors (Krizaj, 1999). Studies on hippocampal pyramidal cells have shown that Caffeine or thapsigargin influences the frequency of miniature IPSCs. Making an assumption, from prior studies described above, that spontaneous Calcium release from pre-synaptic Calcium stores may provide the synchronisation mechanism that causes multivesicular miniature IPSCs and the fact that such a hypothesis has not been tested systematically previously, the authors have taken up this topic for their study on cerebellar interneuron Purkinje cells. This Study   Methods Experiments were conducted on the sagittal cerebellar slices of decapitated rats aged 10-14 days of age. During the experimental recordings, the slices were perfused in saline containing prescribed concentrations of NaCl, KCl, Na H2PO4, NaHCO3, CaCl2, MgCl2 and glucose with 95:5 mixture of oxygen and carbon dioxide. Experiments were done at room temperature. For tight-seal whole-cell recordings, pipettes filled with a solution of appropriate concentrations of CsCl, MgCl2, HEPESCs, BAPTA-Cs (Molecular Probes, Eugene, Oregon), CaCl2, Na-GTP and Na-ATP and of pH 7.3 were used. Capacitance cancellation and series resistance compensation had been done. Kynurenic acid had been added to the extracellular solution to block the inotropic gluatamate receptors. TTX was present in the solution for all recordings. The calcium free solutions were prepared by leaving out Calcium and adding EGTA Na. Membrane potential was maintained at -60mV and the current was filtered at 1.5-2 kHz. Sampling was done continuously with brief interruptions. Detection and analysis were done using the IGOR-Pro programming environment. In experiments needing a Calcium channel blocker, cytochrome was added to the external solution. The toxin was prepared while the ryanodine was purchased. Testing the Calcium The Calcium in the basket cells were tested using the Two-photon laser scanning Fluorescence microscopy. For studying the action potential-evoked calcium increases, bicuculline was added to the external solution and the calcium sensitive probe Oregon Green was put into the pipettes. Scans were done and pulses were applied at the end of each 8th scan. This was repeated every minute in external solution which contained saline in order to get a baseline. The external solution was then changed to the solution containing ryanodine and recording proceeded for another 15 minutes. Another set of recordings were done with external solution not having calcium but having EGTA Na. The internal solution also had EGTA and Cs instead of K as the main cation. The responses in Spontaneous Calcium transients also were recorded using molecular probes in the external solution. A pseudo line scan was also done. For immunocytochemistry, a rabbit polyclonal anti-serum was raised to the 16 amino-acids found in all mammals. A C terminal cysteine enabled conjugation to haemocyanin. The conjugated peptide was used to immunize rabbits. Then the ELISA confirmed the specificity. The sarcoplasmic and endoplasmic reticulum microsomes derived from the skeletal muscle, cardiac tissue, whole brain and cerebellum were used for immunoblot analysis. Effects of external Calcium concentration. Large amplitude miniature IPSCs in cerebellar Purkinje cells were found sensitive to extracellular Calcium. With calcium free solution, the mIPSC frequency fell suddenly to half the control level. Continued exposure to the low level of external calcium caused the frequency of mIPSC to continue declining but at a slower rate. On washing after this, the frequency recovered and reached its initial level. The amplitude of the mIPSCs on the other hand showed a steady decline all through and no recovery on washing. With high levels of Calcium, the frequency of the mIPSCs increased rapidly and significantly. The change in amplitude varied from no response to a minimal increase. The inference was that Calcium strongly influenced mIPSCs in the Purkinje cells though frequency and amplitude were differently affected. The rapid change in frequency was interpreted as the reaction of intracellular Calcium to external Calcium changes. The slow change in amplitude was considered due to the extracellular influence on the pre-synaptic stores. The prolonged extracellular calcium removal could have caused selective elimination of large amplitude miniature IPSCs. Repeating with a calcium-free solution, many large amplitude miniature IPSCs were seen again. Then there was a sudden drop and then the amplitudes reduced to become concurrent with the control and the IPSCs were also less. The reduction seen when external Calcium was removed was not due to post-synaptic modifications. On returning to the calcium-rich solution, a slight recovery of both amplitude and frequency occurred. Paired Student’s t-tests indicate significant changes in mean amplitude and frequency between mIPSCs recorded during a 3-min control period and after 15–18 min in Calcium-free external solution. 6 sham experiments were also conducted by keeping the slices in Calcium containing external solution all throughout and these showed no obvious change. The time course of decay of the IPSCs was slower in calcium-free external solution when compared to depolarization-induced calcium transients. Effects of elevated intracellular Calcium Elevated intracellular Calcium in the Purkinje cells caused a speedy frequency reduction and a slow increase in amplitude. This sudden fall could not be explained by the intracellular calcium as BAPTA buffered the Calcium in the cells and could not have caused the IPSCs. Effect of the axons in large amplitude miniature IPSCs The immediate slow changes in the amplitude of IPSCs on withdrawal of external calcium for 3 minutes could not be attributed to the delayed removal of external calcium from pre-synaptic release sites. The effect was also not due to local Calcium influx caused by the TTX insensitive axonal depolarization. For the latter test, external Cd,   a non-selective channel blocker, was used. It reduced the action potential-evoked pre-synaptic Calcium transients seen in the axons and pre-synaptic terminals of cerebellar interneurons. The slow changes in amplitude were therefore not connected to rundown or altered post-synaptic receptors or delayed extracellular calcium removal. The only remaining explanation was that multivesicular release under the pre-synaptic calcium stores could have caused the changes in amplitude. The lack of recovery after external Calcium restoration could be due to the slow store refilling of intracellular Calcium when action potentials and subsequent calcium influx are blocked. Rise Time Kinetics The multi-vesicular release also could not completely explain the slow changes in amplitude. Rise time of IPSCs as a function of amplitude was studied after extended external calcium removal. In 6 of the 8 cells tested, the rise time was heterogenous in nature where two subpopulations were concerned. Slower decay kinetics was also noted. A faster rise time was seen in the proximal dendrites and soma. Faster IPSCs were more sensitive to external calcium removal than slow ones and these IPSCs arose at somatic synapses. The origin being multivesicular, synchronisation time must have been in the range of submillisecond. Some IPSCs had slower rise time and decays and were less sensitive to external calcium removal. These IPSCs could be arising from dendrites and could be having synchronisation of 1-4ms. Ryanodine receptors The two photon laser illumination was used to focus on the ryanodine receptors stained with a high-affinity Calcium-sensitive dye, Oregon Green BAPTA-1. Transient rises of Calcium in the stained ryanodine receptors in response to short trains of action potentials were measured. The fluorescence rises were noted. Ryanodine-sensitive Calcium stores are associated with the large amplitude mIPSCs. In the experiment Ryanodine in large concentrations of 100 ÃŽ ¼M blocked the receptors. The response recorded showed that Ryanodine reduced the mean amplitude and frequency of mIPSCs simultaneously. The responses to muscimol were not affected by ryanodine and the researchers assumed that ryanodine had no post synaptic effect. Axonal spots with calcium stores were identified in pre-synaptic terminals by recording responses to short action potentials. The intracellular Calcium fluctuations in response to differing concentrations of external calcium to which small concentrations of ryanodine were added was checked. Repeated scanning in the presence of TTX was done. Spontaneous calcium transients were noted before and after addition of ryanodine. Bright spots of fluorescence were noted at the pre-synaptic terminals. This signified the presence and increase of Calcium at the pre-synaptic terminals. Experiments were then done with small concentrations of Ryanodine 10 ÃŽ ¼M. Large amplitude mIPSCs were recorded. High frequency bursts and amplitudes of the responses were greatly increased. The bursts could reflect the response at multivesicular and monovesicular sites. The histogram comparing the amplitudes in the control and after ryanodine was added showed a significant difference. The spontaneous Calcium transients occur at basket cell axons and their frequency was increased by small concentrations of ryanodine.

Status Confessionis and Social Commentary from the Current Church Ess

Status Confessionis and Social Commentary from the Current Church Throughout my ongoing investigation of the interactions between religious values and social behavior, I have become thoroughly intrigued with the role of the institutional church in the realm of social commentary and criticism, as well as political activism. That there is a long standing concept within the church tradition relating to my curiosity is not terribly surprising after just an overview of the language that sociology theory has applied to religious bodies. The role of the church in relation to society is divided into two basic categories of action- that of the â€Å"priest,† and that of the â€Å"prophet.† (Download a PDF file of a pamphlet eslpaining the terminolgoy of "Priest & Prophet.") The former describes the conserving, nurturing actions of the church towards broader social structures, the latter, criticism and the call to move away from corruption towards righteousness. When acting as prophet in the most extreme sense, the church is considered to be in a time of, what is called, status confessionis - acknowledging a state of social injustice so abhorrent that the church must actively interject its influence into even the secular sphere and demand repentance and reform. Nazism and apartheid in South Africa are the two most often cited examples of church bodies acting in status confessionis (Schuurman 100). What intrigues me about this idea is the reserve with which it is invoked, judging by the tone of the passage where the concept is addressed in the book Vocation by Douglas Shuurman. Considering the broader historical-theological context of the issue, including Brunner's injunction against â€Å"‘the disastrous dogma that various ‘orders' are not subj... ...r place in the kingdom of God. On the other hand, as long as the hungry are being fed and the despised loved, God's hand is moving in the world. So I come full circle to find that we must faithfully remain amidst the brokenness and corruption, fix what we can, and be prepared to let God act as God will, as I, and each of us, pursue our own vocations and encourage others to do the same. As theologian Walter Brueggeman has written, â€Å"What God does first and best and most is to trust his people with their moment in history. He trusts them to do what must be done for the sake of the whole community.† So be it. Amen. Works Cited Buechler, Steven M., & F. Kurt Cylke, Jr. Social Movements: Perspectives and Issues . Toronto: Mayfield Publishing Company, 1997. Schuurman, Douglas J. Vocation . Grand Rapids, MI: William B. Eerdmans Publishing Company, 2004.

Illegal Immigration and enforcement of laws Essay

America, as we know it today, is a melting pot of many nationalities, cultures, races, ethnic backgrounds, and religious pursuits. This is the result of the early massive immigration to American shores from countries across the globe seeking a new life inside the borders of the United States. This dream has not waned despite the march of time, with individuals coming from all walks of life, striving to fulfill their dreams of starting a new life for themselves and their families in the United States, or to send them financial support to alleviate the living conditions of their loved ones abroad. But recent times and events have turned the once open gates for these immigrants to closing windows of opportunity as the United States enforces some of the harshest laws primed to keep illegal immigrants from ever setting foot on American soil. The latest battleground for the enforcement of laws regarding the entry and stay of illegal immigrants in the United States is in the state of Arizona. Arizona Senate Bill 1070, the new debatable statute that empowers the police in the state to demand for the papers of any individual that they believe to have illegally entered the United States. Some of the law’s main advocates include the chief of the Maricopa police department, Joe Arpaio and Russell Pearce, the chief sponsor of the bill in the state Senate. Pearce has a personal angle to work for the strict enactment of the bill-Pearce’s son was shot to death by an illegal immigrant (Nathan Thornburgh). As Arizona Governor Jan Brewer affixed his signature to the controversial bill, enacting the same into law within the borders of the state, critics and opponents of the measure guaranteed that the measure’s passage into law will be met with stiff opposition. Many of the opponents of the bill promised stiff legal sanctions and economic boycotts poised to train their guns at Arizona, an event that the state can ill afford as the state is still in the morass of the housing sector collapse that has buffeted the economy of the United States. In the moments before the bill was signed, protesters and police clashed in a rally that has led to minor clashes with authorities, with more than 1,500 people chanting, praying, criticizing or praising Brewer as he began to enact the law. Four of the protesters were taken into custody, after engaging police in a bottle throwing battle, with authorities clad in riot gear (Craig Harris, Alia Beard Rau and Glen Creno). The Republican governor is faced with a vigorous challenge in the primaries and will need the support of the Conservative bloc to hold on to her office, averred that the new statute is one of the new instruments that the state will use in addressing the crisis that they were not responsible in creating, and stated that the Federal government has refused to address this issue at their level. The new legislation has put Arizona squarely in the national spotlight, with no less than United States President weighing in on the matter and CNN broadcasting the signing of the law by Brewer live (Harris, Rau and Creno). In the opinion of Dr. George Weissinger, Ph. D. , the problem with the illegal immigrants coming through the widely porous border regions of the United States with its southern neighbor is a dilemma that is not confined to the problem with U. S. -Mexico immigration problems, and opines that the enforcement of the present set of immigration laws by the United States government only contributes to the ever-increasing illegal immigrant population of the United States. Weissinger (2003) argues that much of the societal perceptions of the illegal alien in the United States vary from the sympathetic to the bigoted. With this type of confusion on the response of the society to the true plight of the illegal immigrants entering the United States, the responses as mentioned above are to be expected (Weissinger). What is considered to be a prime catalyst in the formation of the opinions of the society against or for the illegal immigrants is the media; the media usually characterizes the illegal alien as one who crosses over the border of his own country to the next, with nothing more spurring him/her on than the possibility of being able to find a means of employment that will allow them to fend for their families back in their own native lands. But with the events that occurred that tragic day on the 11th of September, 2001, the image of the illegal alien has radically been transformed. The media is a powerful conveyor of the way that the illegal immigrant is portrayed in American or any other society. When the news broadcast images of immigrant day laborers, this image will serve as the standard by which society deems what it defines to be the image of the illegal aliens in the society (Weissinger). Many of these characterizations are more inclined on the aesthetics rather than the economic, health or issues that deal with conflicts with the law. Many residents in the area that illegal immigrant congregate usually fear a decrease in their property values, or even some have the notion that the illegal immigrants might become a hindrance to their business activities. These illegal immigrants flock to many locations in the United States where they hope that potential employers will hire them for the day, thus allowing them to send some financial aid to their families back home. But even without the Arizona and California laws, there is ample laws provided to the Federal government to deal with the problem of illegal immigrants (Weissinger). The Immigration and Naturalization Service (INS), under Title 8 USC Section 1357, has appointed officers and other personnel to implement the law on illegal immigrants, allowing them the mandate to question suspected illegal immigrants with regards to their continued stay in the United States, even without the benefit and requirement of a warrant. But unfortunately, the agency has been remiss in this duty to address this problem even before the enactment of the controversial Arizona statute. In the operating policy of the INS, now officially known as the Bureau of Immigration and Customs Enforcement (BICE), the target of the body is not the illegal immigrants themselves, but the employers who hire these illegal immigrants, removing the demand, and not the supply, in an effort to discourage illegal immigrants from coming to the United States to find employment. These operating policies developed as a result of the implementation of the 1986 Immigration Reform and Control Act (Weissinger). But Arizona is not alone among the states of the Union trying to address their problems with regards to the burgeoning number of illegal aliens in their states. The Washington Times, known as a conservative publication, has recently reported that the illegal immigrant statute in California is akin to the one being enacted and implemented in Arizona. The Post reports that in the Penal Code of California, section 834b, states that California law enforcement units should fully cooperate with the United States Immigration and Naturalization Service (INS) with regards to any individual that is taken into custody if the person is allegedly in the United States under the premise on infringing existing United States immigration laws. Advocates of the Arizona law aver that the basis of the law in the state simply follows the gist of existing Federal statutes regarding illegal immigrants. Laws that have been implemented by the Federal government for the past seven decades. The text of the California section reads as follows: With respect to any such person who is arrested, and suspected of being present in the United States in violation of federal immigration laws, every law enforcement agency shall do the following: (1) Attempt to verify the legal status of such person as a citizen of the United States, an alien lawfully admitted as a permanent resident, an alien lawfully admitted for a temporary period of time or as an alien who is present in the United States in violation of immigration laws. The verification process may include, but shall not be limited to, questioning the person regarding his or her date and place of birth, and entry into the United States, and demanding documentation to indicate his or her legal status (Dennis Romero). George Orwell, author of such works as â€Å"Animal Farm† and â€Å"1984†, states that one of the great tragedies in crafting such important legislation, is that thousands of dollars in taxpayer’s money are wasted in crafting these laws. Many eagerly anticipate for the passage of the law, then downgrade the importance of actually enforcing the law itself. In the time that the debate on the need of the law in the first place, the very thing that the law was crafted for in the first place remains and grows, becoming part and parcel of the life of the society. Until such time that the issue has become too damaging to the society, it is only in that time that the law will be once again resurrected to address the problem, which could have been addressed if the law was enforced earlier (Arizona Immigration Laws). The law that empowered the INS/BICE to enforce the laws on immigration was originally crafted by the United States Congress, with both houses giving unanimous support to the immigration bills, as the laws were enacted in the early years of the 20th century. The laws against illegal immigration were rendered to the hands of the President of the United States, with the belief that the Executive branch will be able to faithfully execute the tenets of the law. The enforcement of the laws went smoothly until the 1960’s, when the implementation of the civil rights laws in the United States and the rigorous enforcement of the laws regulating Hispanic immigration into America found themselves at loggerheads in the political circle. Unfortunately, the law against the entry of illegal immigrants coming from the southern American neighbors, particularly Hispanic immigrants, was overthrown to accommodate the caprices of United States Democrat senators, caring more for the support of the affluent farmers in their constituencies than assuring that the laws against the entry of illegal immigrants into the United States was conscientiously enforced (Arizona). But are immigrants actually those that are in violation of United States immigration laws? According to Dr. Weissinger (2003), those that violate immigration laws are not considered as immigrants. In his opinion, there is a wide degree of differentiation against those that willingly infringe on the laws of the United States, and those immigrants that apply for residency in the United States, faithfully complying with the many requirements needed to gain legal citizenship in the United States. The confusion between the two contributes to the illogical responses and connotations attached to the illegal issue and picturing these two as equal issues is the result of dubious logic (Weissinger). The emphasis of the current administration on the strict, unyielding enforcement of the immigration laws has given way to a increased number of deportations by the BICE. In the statement of ICE assistant secretary John Morton, ICE is expected to acquire the needed resources and logistics that will allow the agency to deport more than 400,000 illegal immigrants in 2010. This figure, according to Morton, is an increase of 10 percent over the figures posted the previous year. In addition, increasing numbers of raids on companies and businesses that are allegedly contracting the services of illegal immigrants have registered an increase of nearly four times than the entire administration of former President George W. Bush. In the statement of the ICE, the priority of the agency is the location, arrest and eventual deportation of convicted criminals and other lawless elements in the United States illegally (Jurist Legal News and Research Services, Inc. ). The Department of Homeland Security is also fine tuning its resources intended to enforce Federal immigration laws, revising its 287g program, that gave a mandate to local police authorities to implement immigration statutes, which is considered one of the more disputable aspects of American border policy. But critics of the program aver that the program, originally intended to determine the identity of criminals in the United States in violation of immigration laws, has led to racial profiling by the police authorities in the areas where immigrants abound. They aver that the law gave the power to law enforcement authorities to arrest illegal immigrants even om such minor citations as a broken tail light. But many of the supporters aver the efficaciousness of the program, saying the program has become an effective tool in addressing the problem of illegal immigration (Miriam Jordan). In the new policy to be released by the DHS, the powers of the police to interrogate and arrest illegal immigrants, with the intent of preventing sheriff and police personnel to accost suspected illegal immigrants on the premise that they have violated some fictitious infarction as a means of initiating deportation proceedings against the individual. In the last two years, according to the data released by the Homeland Security Department, approximately 120,000 alleged illegal immigrants were identified with the use of the program, with the majority of the cases ending in deportation of the suspected illegal immigrant. Arpaio, one of the staunchest supporters of the Arizona illegal immigrants law, is also considered one of the most active enforcers of the program on the local level. But the Maricopa sheriff is under investigation by no less than the United States Department of Justice, investigating claims that Maricopa sheriff deputies have utilized skin color as a front to detain Hispanics that they believe are illegal immigrants (Jordan). With approximately 10. 8 million illegal immigrants in the United States, the issue of immigration is considered to be one of the most heavily debated issues in the United States. The Arizona statute, regarded as the harshest measure enacted by a state in recent history against the problem of illegal immigrants, requires that local police establish the fact that a person is an illegal immigrant, that they have logical basis to do so, and to place under police custody those individuals who fail to prove or to present documents that they are in the United States legally. Under the law, the acts of transporting an illegal immigrant and to hire day laborers are also penalized. In the opinion of Senator Pearce, he believes that handcuffs, used on the ‘right’ individuals, can be considered as an effective crime fighting tool (Tim Gaynor, David Schwartz). At present, there is a large number of undocumented illegal immigrants in the United States. Spread across such states as California, New Mexico, Arizona, and Texas, the number of illegal immigrants, those that are here to find work and also those who are in America for more nefarious ends, continues to expand due to the reluctance of the Federal government to adequately and faithfully enforce United States laws on illegal immigration. As such, they are becoming burdensome on the systems of the United States; health care, welfare, education, employment and other programs of the Federal government, resources that should have been used for those that are in the United States legally and for its citizens (Arizona). Works Cited Arizona Immigration Law. â€Å"The Dilemma of Illegal Immigrtion: Enforcment of Current Federal/ State Laws versus Reform. † Gaynor, Tim, Schwartz, David. â€Å"Arizona passes tough illegal immigration law†. Harris, Craig, Rau, Alia Beard, Creno, Glen, â€Å"Arizona govenor signs immigration law; foes promise fight†. Arizona Republic. 24 April 2010. Jordan, Miriam. â€Å"New Curbs Set on Arrests of Illegal Immigrants†. Wall Street Journal 11 July 2009. Jurist Legal News and Research Services, Inc. â€Å"US government increasing enforcement of immigration laws: report†. Romero, Dennis. â€Å"California’s Illegal-Immigration Enforcement Law is Tougher than Arizona’s†. Thornburgh, Nathan. â€Å"Arizona Police Split on Immigration Crackdown†. Time Magazine 30 April 2010. Weissinger, George, Ph. D. â€Å"The Illegal Alien Problem: Enforcing the Immigration Laws†.

What are Exponential Growth Functions

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. The following focuses on using exponential growth functions to make predictions. Exponential Growth Exponential growth is the change that occurs when an original amount is increased by a consistent rate over a period of time Uses of Exponential Growth in Real Life: Values of home pricesValues of investmentsIncreased membership of a popular social networking site Exponential Growth in Retail Edloe and Co. relies on word of mouth advertising, the original social network. Fifty shoppers each told five people, and then each of those new shoppers told five more people, and so on. The manager recorded the growth of store shoppers. Week 0: 50 shoppersWeek 1: 250 shoppersWeek 2: 1,250 shoppersWeek 3: 6,250 shoppersWeek 4: 31,250 shoppers First, how do you know that this data represents exponential growth? Ask yourself two questions. Are the values increasing? YesDo the values demonstrate a consistent percent increase? Yes. How to Calculate Percent Increase Percentage increase: (Newer - Older)/(Older) (250 - 50) / 50 200/50 4.00 400% Verify that the percentage increase persists throughout the month: Percentage increase: (Newer - Older)/(Older) (1,250 - 250)/250 4.00 400%Percentage increase: (Newer - Older)/(Older) (6,250 - 1,250)/1,250 4.00 400% Careful - do not confuse exponential and linear growth. The following represents linear growth: Week 1: 50 shoppersWeek 2: 50 shoppersWeek 3: 50 shoppersWeek 4: 50 shoppers Note: Linear growth means a consistent number of customers (50 shoppers a week); exponential growth means a consistent percent increase (400%) of customers. How to Write an Exponential Growth Function 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. Fill in the blanks: a 50 shoppersb 4.00 y 50(1 4)x Note: Dont fill in values for x and y. The values of x and y will change throughout the function, but the original amount and percent change will remain constant. Use the Exponential Growth Function to Make Predictions Assume that the recession, the primary driver of shoppers to the store, persists for 24 weeks. How many weekly shoppers will the store have during the 8th week? Careful, do not double the number of shoppers in week 4 (31,250 *2 62,500) and believe its the correct answer. Remember, this article is about is exponential growth, not linear growth. Use Order of Operations to simplify. y 50(1 4)x y 50(1 4)8 y 50(5)8 (Parenthesis) y 50(390,625) (Exponent) y 19,531,250 (Multiply) 19,531,250 shoppers Exponential Growth in Retail Revenues Prior to the start of the recession, the stores monthly revenue hovered around $800,000. A stores revenue is the total dollar amount that customers spend in the store on goods and services. Edloe and Co. Revenues Prior to recession: $800,0001 month after recession: $880,0002 months after recession: $968,0003 months after recession: $1,171,2804 months after recession: $1,288,408 Exercises Use the information about Edloe and Cos revenues to complete 1 through 7. What are the original revenues?Whats the growth factor?How does this data model exponential growth?Write an exponential function that describes this data.Write a function to predict revenues in the fifth  month after the start of the recession.What are the revenues in the fifth  month after the start of the recession?Assume that the domain of this exponential function is 16 months. In other words, assume that the recession will last for 16 months. At what point will revenues surpass 3 million dollars?