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Unit 5: Mathematical Recursion - Assignment




Question;Unit 5;Mathematical Recursion - Assignment;Total;points for Assignment: 35 points.;Assignments;must be submitted as a Microsoft Word document and uploaded to the Dropbox for;Unit 5.;All Assignments are due by Tuesday at 11:59 PM ET of the assigned Unit.;NOTE: Assignment problems should not be posted to the Discussion threads.;Questions on the Assignment problems should be addressed to the instructor by;sending an email or by attending office hours.;You must;show your work on all problems. If a problem is worth 2 points and you;only show the answer, then you will receive only 1 point credit. If;you use a calculator or online website, give the source and tell me exactly;what you provided as input. For example, if you used Excel to;compute 16 * 16, state ?I typed =16*16 into Excel and got 256. You;may type your answer right into this document.;Part;I. Basic Computations;1.;According to the National Education Association[1], the average classroom;teacher in the US earned $43,837 in annual salary for the 1999-2000 school;year.;a.;If the teachers receive an average salary increase of $1096, write out the;first 6 terms of the sequence formed by the average salaries starting with the;1999-2000 school year. Explain how you got your answer. (1;point);Answer;Explanation;b.;Write the general form for the sequence. (1 point);Answer;Explanation;c.;Write the recursive formula for an. (1 point);Answer;Explanation;2.;In 1965, Gordon Moore, the cofounder of Intel, predicted that the number of;transistors that could be designed into an integrated circuit would double;every two years[2]. This result is known as Moore?s Law.;a.;Complete the following table, showing the number of transisters per circuit for;the indicated years.;(1 point);Year;Number of Transistors;1972;2500;1974;1976;1978;1980;1982;1984;1986;1988;1990;b.;Express this sequence using a recursive formula in which we can express any;term an in terms of the term an-2 (the term 2 years;prior). [Hint: Remember that n represents the number of years since;1970, since n = 2 represents the year 1972. ] (1 point);Answer;Explanation;c.;According to Intel, the Pentium 4 processor circuit, released in the year 2000;is designed using 42,000,000 transistors. According to your;calculations, is this circuit consistent with Moore?s Law? Explain your;answer. (1 point);Answer;Explanation;3.;Expand the following summation, then evaluate. In your explanation;describe the steps involved in arriving at your answer. (5 points);Answer;Explanation;4.;The sequence formed by the Lucas;numbers is as follows:. Using proper terminology as you;learned in this unit, compare and contrast the Lucas sequence with the famous Fibonacci;sequence by naming at least one similar property and one contrasting;property. (4 points);Answer;Part;II. Case Study;The Mystery of the Missing Coulomb;This week;Patty Madeye is going to be investigating the theft of a rare Orange Tiger;Coulomb (shown at the right), which is owned by Madame Levare, who lives in;West Floflux.;Since the;jewels are quite valuable, Madam Levare stores them in the vault at the;jeweler?s store, West FloFlux GemStone in downtown West FloFlux.;Only certain lockboxes in the vault were touched ? it seems;that the thief knew exactly what he was looking for.;Task #1 ?;Patty?s first task is to determine the value of the jewels. She talks to;the jeweler who created them and he estimates the value of the jewels in 1985;(when they were purchased) at $65,000. The value is thought to increase;(appreciate) by $1500 per year. If this is true, how much would the;jewels be worth in 2010? Explain how you arrived at your answer. (4;points);Answer;Explanation;Task #2;- Patty talks to the jeweler and discovers that he remembers the 4-digit;combination to the main vault in the store by writing it down in summation;form. Here?s what he wrote;The combination;is written in summation form, but some of the notation is cut off from where;the paper is ripped. You?ll need to figure out the full equation so that;Patty can get into the vault to investigate. (4 points);Answer;Explanation;Task #3;- Patty notices a pattern in the numbers of the lockboxes that were;touched during the robbery and says that she thinks that it?s a;mathematical sequence. The sequence is { 8, 15, 22, 29;?}. Determine whether this is a sequence (as far as you can;tell) and what type (arithmetic or geometric) it is.;Justify your answer by stating the general term for the sequence.;Assuming Patty is correct, can you identify two other lockboxes that might have;been emptied using this sequence? (4 points);Answer;Explanation;Task;#4 (8 points) ? Patty asks you to find out more information about the;Fibonacci sequence as background for this week?s episode. Do some;research on the Fibonacci numbers by consulting the Kaplan Library or the;internet. Find two facts or interesting properties about this fascinating;topic and write a 1 page essay describing what you have found. Possible;approaches include;-;The origin of the Fibonacci sequence?;-;What is the connection between the Fibonacci sequence and the golden ratio?;-;Does the ?golden string? ever repeat?;Answer;Essay Requirements;-;Write your essay in this document ? do not save it in a separate file.;-;Your answer should be between 400-500 words (about 1 page of double-spaced;text);-;You must cite all sources (book, website, periodical) using APA format, however;do not use unreliable sources such as Wikipedia, and Yahoo! Answers.


Paper#60825 | Written in 18-Jul-2015

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