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[17.58.23.197]) by mx.google.com with ESMTPS id r27si20831885pgb.408.2021.01.25.11.20.08 for (version=TLS1_2 cipher=ECDHE-ECDSA-AES128-GCM-SHA256 bits=128/128); Mon, 25 Jan 2021 11:20:18 -0800 (PST) Received-SPF: pass (google.com: domain of prowellhannah@icloud.com designates 17.58.23.197 as permitted sender) client-ip=17.58.23.197; Authentication-Results: mx.google.com; dkim=pass header.i=@icloud.com header.s=1a1hai header.b=hlxZWwSq; spf=pass (google.com: domain of prowellhannah@icloud.com designates 17.58.23.197 as permitted sender) smtp.mailfrom=prowellhannah@icloud.com; dmarc=pass (p=QUARANTINE sp=QUARANTINE dis=NONE) header.from=icloud.com DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=icloud.com; s=1a1hai; t=1611602406; bh=xTMs/oqD9kEjlKxj6yQciMKt6kaZS61fWiDzYbf3SkY=; h=From:Content-Type:Mime-Version:Subject:Message-Id:Date:To; b=hlxZWwSqFyOcLL7LzcX/DZflK+EpF97SWlyYNkOMiePjQdOpW4mpUW2FwG5YKucRY FAHymJqgSXdgIlzMRrdDHonVjMZvZn447I87mM+lUqylFl7jhNPiNnB45+tHam9v0W Gd4NtgrGWk/JVQYCFDhgYF8NWqhcoaCe+UviItUNmjqP72pksniALErql6I1siOIN+ feHScJsvql1NRYW9QAmjZ3Mn5bBUOQd3bO6OQGpHLdiOkXV2GtMmu2tfW1nBTgHWBf uFWSUtQz8cEN2V6TeDMjbkJ4hSushIRF74VzBgcFJWW5iXO3AVp5YwOOLQB+WHI+Zw F3Xv2pxg0rTYg== Received: from [IPv6:2607:fb90:4ed7:a08b:180c:8a85:5329:229b] (unknown [172.58.30.205]) by mr85p00im-zteg06012001.me.com (Postfix) with ESMTPSA id E40BDA00292 for ; Mon, 25 Jan 2021 19:20:01 +0000 (UTC) From: Hannah Prowell Content-Type: multipart/alternative; boundary="Apple-Mail=_7470FA5A-0320-46A6-A260-6C294B7CD311" Mime-Version: 1.0 (Mac OS X Mail 12.4 \(3445.104.15\)) Subject: HW Message-Id: <325CF399-597D-43A4-8397-B660C1092196@icloud.com> Date: Mon, 25 Jan 2021 11:19:56 -0800 To: Hannah Prowell X-Mailer: Apple Mail (2.3445.104.15) X-Proofpoint-Virus-Version: vendor=fsecure engine=2.50.10434:6.0.343,18.0.737 definitions=2021-01-25_08:2021-01-25,2021-01-25 signatures=0 X-Proofpoint-Spam-Details: rule=notspam policy=default score=0 suspectscore=0 malwarescore=0 phishscore=0 bulkscore=0 spamscore=0 clxscore=1015 mlxscore=0 mlxlogscore=909 adultscore=0 classifier=spam adjust=0 reason=mlx scancount=1 engine=8.0.1-2006250000 definitions=main-2101250101 --Apple-Mail=_7470FA5A-0320-46A6-A260-6C294B7CD311 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=utf-8 1. Marko currently has 20 tulips in his yard. Each year he plants 5 = more.=20 a. Write a recursive formula for the number of tulips Marko has=20 b. Write an explicit formula for the number of tulips Marko has 3. A store=E2=80=99s sales (in thousands of dollars) grow according to = the recursive rule Pn=3DPn-1 + 15, with initial population P0=3D40.=20 a. Calculate P1 and P2=20 b. Find an explicit formula for Pn c. Use your formula to predict the = store=E2=80=99s sales in 10 years d. When will the store=E2=80=99s sales = exceed $100,000? 5. A population of beetles is growing according to a linear growth = model. The initial population (week 0) was P0=3D3, and the population = after 8 weeks is P8=3D67.=20 a. Find an explicit formula for the beetle population in week n=20 b. After how many weeks will the beetle population reach 187? 7. Tacoma's population in 2000 was about 200 thousand, and had been = growing by about 9% each year.=20 a. Write a recursive formula for the population of Tacoma=20 b. Write an explicit formula for the population of Tacoma=20 c. If this trend continues, what will Tacoma's population be in 2016?=20 d. When does this model predict Tacoma=E2=80=99s population to exceed = 400 thousand? 9. Diseases tend to spread according to the exponential growth model. In = the early days of AIDS, the growth rate was around 190%. In 1983, about = 1700 people in the U.S. died of AIDS. If the trend had continued = unchecked, how many people would have died from AIDS in 2005? 17. The population of a small town can be described by the equation Pn =3D= 4000(1.04)n , where n is the number of years after 2005. Explain in = words what this equation tells us about how the population is changing.=20= Most of the examples in the text examined growing quantities, but linear = and exponential equations can also describe decreasing quantities, as = the next few problems will explore 19. Inflation causes things to cost more, and for our money to buy less = (hence your grandparents saying, "In my day, you could buy a cup of = coffee for a nickel"). Suppose inflation decreases the value of money by = 5% each year. In other words, if you have $1 this year, next year it = will only buy you $0.95 worth of stuff. How much will $100 buy you in 20 = years? 35. Describe, using your own words, what happens to the energy of an = earthquake each time the magnitude on the Richter scale increases by 1. 36. Remember that log (M) is the exponent so that 10 to that exponent is = M. Given this fact, find=20 a. log (1000)=20 b. log (10)=20 c. log (10,000,000) 37. As mentioned in the text, the 1994 Northridge Earthquake registered = a 6.7 on the Richter scale. In July, 2019, there was a major earthquake = in Ridgecrest, California, with a magnitude of 7.1. How much bigger was = the Ridgecrest quake compared to the Northridge Earthquake 25 years = before (in terms of the energy released)? Use a calculator.=20 1. One side of a circular cylinder, a rectangular box, a triangular = prism are shown below. Connect each vertex with the principal vanishing = point to draw the cylinder, box, and prism. 2. Suppose you are sitting at the end of a long hallway, where the = ceiling has rectangular panels ,the floor has square tiles, and the two = side walls have vertical lines every few feet. Draw the hallway from = your perspective, with a principal vanishing point. Now, what happens if = you stand up? How would your picture change? How about if you move to = the left? 3. Do some online research to find which artists seem to have used the = Golden Ratio in their works of art. Give some examples of their art = pieces.=20 4. Do some online research to find which composers seem to have written = music that reflects the Golden Ratio. Give some specific examples of = their music works.=20 5. Do some online research on the Golden Rectangle. Why is this called = =E2=80=9Cgolden=E2=80=9D? Where do we see Golden Rectangles around us?=20= 6. The Fibonacci Sequence begins with 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, = 89, =E2=80=A6 List the next three Fibonacci numbers (the next three = terms of this sequence).=20 7. Do some online research on the Fibonacci Sequence. Find its = relationship to the biological world, such as pine cones, sunflowers, = nautilus shells, and human bodies.=20 9. A guitarist tunes his first (thinnest) string at E =3D 330 cps = (typically denoted =E2=80=9CE4=E2=80=9D). If his sixth (thickest) string = is to be two octaves lower, what is the frequency of the sixth string? 11. If A =3D 440 cps, the real =E2=80=9Cperfect fifth=E2=80=9D would be = E, whose frequency would be exactly 3/2 of A. What frequency is that? = Compare that with the =E2=80=98tempered=E2=80=9D frequency of E. 14. It is said that Mariah Carey can hit a note as low as F2 and as high = as G7 (slightly more than five octaves). Find the frequencies that cover = this range. (Assume =E2=80=9CA4=E2=80=9D is 440 cps. A3 is half of it. = A2 is half of that frequency. F2 is even lower. The numerical portion = increases by 1 for each octave, and a new number starts with a C. So, = for instance, the sequence goes like this: A2, A2#, B2, C3, C3#, =E2=80=A6= ) 255 | Math 100 Using the initiator and generator shown, draw the next = two stages of the iterated fractal. 1. A college offers tutoring in Math, English, Chemistry, and Biology. = The number of students enrolled in each subject is listed below. If the = college can only afford to hire 15 tutors, determine how many tutors = should be assigned to each subject. Math: 330 English: 265 Chemistry: = 130 Biology: 70 7. A small country consists of five states, whose populations are listed = below. If the legislature has 119 seats, apportion the seats.=20 A: 810,000=20 B: 473,000=20 9. A small country consists of three states, whose populations are = listed below. A: 6,000 B: 6,000 C: 2,000=20 a. If the legislature has 10 seats, use Hamilton=E2=80=99s method to = apportion the seats.=20 b. If the legislature grows to 11 seats, use Hamilton=E2=80=99s method = to apportion the seats.=20 c. Which apportionment paradox does this illustrate? 11. A school district has two high schools: Lowell, serving 1715 = students, and Fairview, serving 7364. The district could only afford to = hire 13 guidance counselors.=20 a. Determine how many counselors should be assigned to each school using = Hamilton's method.=20 b. The following year, the district expands to include a third school, = serving 2989 students. Based on the divisor from above, how many = additional counselors should be hired for the new school?=20 c. After hiring that many new counselors, the district recalculates the = reapportion using Hamilton's method. Determine the outcome.=20 d. Does this situation illustrate any apportionment issues? 51. To decide on a movie to watch, a group of friends all vote for one = of the choices (labeled A, B, and C). The individual ballots are shown = below.=20 Create a preference table. CAB, CBA, BAC, BCA, CBA, ABC, ABC, CBA, BCA, = CAB, CAB, BAC 53. A non-profit agency is electing a new chair of the board. The votes = are shown below.=20 Number of=20 voters: 11 5 10 3=20 1st choice: Atkins Cortez Burke Atkins=20 2nd choice: Cortez Burke Cortez Burke=20 3rd choice: Burke Atkins Atkins Cortez=20 a. How many voters voted in this election?=20 b. How many votes are needed for a majority? A plurality?=20 c. Find the winner under the plurality method.=20 d. Find the winner under the Borda Count Method.=20 e. Find the winner under the Instant Runoff Voting method.=20 f. Find the winner under Copeland=E2=80=99s method. 55. The homeowners association is deciding a new set of neighborhood = standards for architecture, yard maintenance, etc. Four options have = been proposed. The votes are:=20 Number of voters 8 9 11 7 7 5=20 1st choice B A D A B C=20 2nd choice C D B B A D=20 3rd choice A C C D C A=20 4th choice D B A C D B=20 a. How many voters voted in this election?=20 b. How many votes are needed for a majority? A plurality?=20 c. Find the winner under the plurality method.=20 d. Find the winner under the Borda Count Method.=20 e. Find the winner under the Instant Runoff Voting method.=20 f. Find the winner under Copeland=E2=80=99s method. 57. Consider an election with 953 votes.=20 c. If there are 7 candidates, what is the smallest number of votes that = a plurality candidate could have?=20 d. If there are 8 candidates, what is the smallest number of votes that = a plurality candidate could have? 59. Does this voting system having a Condorcet Candidate? If so, find = it.=20 Number of voters 8 7 6=20 1st choice A C B=20 2nd choice B B C=20 3rd choice C A A 61. The downtown business association is electing a new chairperson, and = decides to use approval voting. The tally is below, where each column = shows the number of voters with the particular approval vote. Which = candidate wins under approval voting?=20 Number of voters 8 7 6 3 4 2 5=20 A X X X X (8,7,4,5) B X X X X (8,6,3,5) C X X X X (7,6,3,2) D X X X X. (8,6,4,2) --Apple-Mail=_7470FA5A-0320-46A6-A260-6C294B7CD311 Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset=utf-8


1. Marko currently has 20 tulips in his yard. Each = year he plants 5 more. 


a. Write a recursive formula for the number of tulips = Marko has 


b. Write an explicit formula for the number of tulips = Marko has


3. A store=E2=80=99s sales (in thousands of dollars) = grow according to the recursive rule Pn=3DPn-1 + 15, with initial = population P0=3D40. 


a. Calculate P1 and P2 


b. Find an explicit formula for Pn c. Use your formula = to predict the store=E2=80=99s sales in 10 years d. When will the = store=E2=80=99s sales exceed $100,000?


5. A population of beetles is growing according to a = linear growth model. The initial population (week 0) was P0=3D3, and the = population after 8 weeks is P8=3D67. 


a. Find an explicit formula for the beetle population = in week n 


b. After how many weeks will the beetle population = reach 187?


7. Tacoma's population in 2000 was about 200 thousand, = and had been growing by about 9% each year. 


a. Write a recursive formula for the population of = Tacoma 


b. Write an explicit formula for the population of = Tacoma 


c. If this trend continues, what will Tacoma's = population be in 2016? 


d. When does this model predict Tacoma=E2=80=99s = population to exceed 400 thousand?


9. Diseases tend to spread according to the = exponential growth model. In the early days of AIDS, the growth rate was = around 190%. In 1983, about 1700 people in the U.S. died of AIDS. If the = trend had continued unchecked, how many people would have died from AIDS = in 2005?


17. The population of a small town can be described by = the equation Pn =3D 4000(1.04)n , where n is the number of years after = 2005. Explain in words what this equation tells us about how the = population is changing. 


Most of the examples in the text examined growing = quantities, but linear and exponential equations can also describe = decreasing quantities, as the next few problems will explore


19. Inflation causes things to cost more, and for our = money to buy less (hence your grandparents saying, "In my day, you could = buy a cup of coffee for a nickel"). Suppose inflation decreases the = value of money by 5% each year. In other words, if you have $1 this = year, next year it will only buy you $0.95 worth of stuff. How much will = $100 buy you in 20 years?


35. Describe, using your own words, what happens to = the energy of an earthquake each time the magnitude on the Richter scale = increases by 1.


36. Remember that log (M) is the exponent so that 10 = to that exponent is M. Given this fact, find 


a. log (1000) 


b. log (10) 


c. log (10,000,000)


37. As mentioned in the text, the 1994 Northridge = Earthquake registered a 6.7 on the Richter scale. In July, 2019, there = was a major earthquake in Ridgecrest, California, with a magnitude of = 7.1. How much bigger was the Ridgecrest quake compared to the Northridge = Earthquake 25 years before (in terms of the energy released)? Use a = calculator. 


1. One side of a circular cylinder, a rectangular box, = a triangular prism are shown below. Connect each vertex with the = principal vanishing point to draw the cylinder, box, and = prism.


2. Suppose you are sitting at the end of a long = hallway, where the ceiling has rectangular panels ,the floor has square = tiles, and the two side walls have vertical lines every few feet. Draw = the hallway from your perspective, with a principal vanishing point. = Now, what happens if you stand up? How would your picture change? How = about if you move to the left?


3. Do some online research to find which artists seem = to have used the Golden Ratio in their works of art. Give some examples = of their art pieces. 


4. Do some online research to find which composers = seem to have written music that reflects the Golden Ratio. Give some = specific examples of their music works. 


5. Do some online research on the Golden Rectangle. = Why is this called =E2=80=9Cgolden=E2=80=9D? Where do we see Golden = Rectangles around us? 


6. The Fibonacci Sequence begins with 1, 1, 2, 3, 5, = 8, 13, 21, 34, 55, 89, =E2=80=A6 List the next three Fibonacci numbers = (the next three terms of this sequence). 


7. Do some online research on the Fibonacci Sequence. = Find its relationship to the biological world, such as pine cones, = sunflowers, nautilus shells, and human bodies. 


9. A guitarist tunes his first (thinnest) string at E = =3D 330 cps (typically denoted =E2=80=9CE4=E2=80=9D). If his sixth = (thickest) string is to be two octaves lower, what is the frequency of = the sixth string?


11. If A =3D 440 cps, the real =E2=80=9Cperfect = fifth=E2=80=9D would be E, whose frequency would be exactly 3/2 of A. = What frequency is that? Compare that with the =E2=80=98tempered=E2=80=9D = frequency of E.


14. It is said that Mariah Carey can hit a note as low = as F2 and as high as G7 (slightly more than five octaves). Find the = frequencies that cover this range. (Assume =E2=80=9CA4=E2=80=9D is 440 = cps. A3 is half of it. A2 is half of that frequency. F2 is even lower. = The numerical portion increases by 1 for each octave, and a new number = starts with a C. So, for instance, the sequence goes like this: A2, A2#, = B2, C3, C3#, =E2=80=A6) 255 | Math 100 Using the initiator and generator = shown, draw the next two stages of the iterated fractal.


1. A college offers tutoring in Math, English, = Chemistry, and Biology. The number of students enrolled in each subject = is listed below. If the college can only afford to hire 15 tutors, = determine how many tutors should be assigned to each subject. Math: 330 = English: 265 Chemistry: 130 Biology: 70


7. A small country consists of five states, whose = populations are listed below. If the legislature has 119 seats, = apportion the seats. 


A: 810,000 


B: 473,000 


9. A small country consists of three states, whose = populations are listed below. A: 6,000 B: 6,000 C: 2,000 


a. If the legislature has 10 seats, use Hamilton=E2=80=99= s method to apportion the seats. 


b. If the legislature grows to 11 seats, use = Hamilton=E2=80=99s method to apportion the seats. 


c. Which apportionment paradox does this = illustrate?


11. A school district has two high schools: Lowell, = serving 1715 students, and Fairview, serving 7364. The district could = only afford to hire 13 guidance counselors. 


a. Determine how many counselors should be assigned to = each school using Hamilton's method. 


b. The following year, the district expands to include = a third school, serving 2989 students. Based on the divisor from above, = how many additional counselors should be hired for the new school? 


c. After hiring that many new counselors, the district = recalculates the reapportion using Hamilton's method. Determine the = outcome. 


d. Does this situation illustrate any apportionment = issues?


51. To decide on a movie to watch, a group of friends = all vote for one of the choices (labeled A, B, and C). The individual = ballots are shown below. 


Create a preference table. CAB, CBA, BAC, BCA, CBA, = ABC, ABC, CBA, BCA, CAB, CAB, BAC


53. A non-profit agency is electing a new chair of the = board. The votes are shown below. 


Number of 


voters:   =       11   5   10   3 


1st choice: Atkins Cortez Burke Atkins 


2nd choice: Cortez Burke Cortez Burke 


3rd choice: Burke Atkins Atkins Cortez 


a. How many voters voted in this election? 


b. How many votes are needed for a majority? A = plurality? 


c. Find the winner under the plurality method. 


d. Find the winner under the Borda Count Method. 


e. Find the winner under the Instant Runoff Voting = method. 


f. Find the winner under Copeland=E2=80=99s method.


55. The homeowners association is deciding a new set = of neighborhood standards for architecture, yard maintenance, etc. Four = options have been proposed. The votes are: 


Number of voters 8 9 11 7 7 5 


    =         1st choice B A D A B C 


    =       2nd choice C D B B A D 


    =       3rd choice A C C D C A 


   =       4th choice D B A C D B 


a. How many voters voted in this election? 


b. How many votes are needed for a majority? A = plurality? 


c. Find the winner under the plurality method. 


d. Find the winner under the Borda Count Method. 


e. Find the winner under the Instant Runoff Voting = method. 


f. Find the winner under Copeland=E2=80=99s = method.



57. Consider an election with 953 votes. 


c. If there are 7 candidates, what is the smallest = number of votes that a plurality candidate could have? 


d. If there are 8 candidates, what is the smallest = number of votes that a plurality candidate could have?


59. Does this voting system having a Condorcet = Candidate? If so, find it. 


Number of voters 8 7 6 


   =         1st choice A C B 


   =       2nd choice B B C 


   =       3rd choice C A A


61. The downtown business association is electing a = new chairperson, and decides to use approval voting. The tally is below, = where each column shows the number of voters with the particular = approval vote. Which candidate wins under approval voting? 


Number of voters 8 7 6 3 4 2 5 


   =                     =     A X X   =     X  =   X  = (8,7,4,5)


   =                     =     B X  =   X X     =   X  = (8,6,3,5)


    =                     =   C   X X = X         = X  = (7,6,3,2)


   =                     =     D X   = X   X X.      = (8,6,4,2)















= --Apple-Mail=_7470FA5A-0320-46A6-A260-6C294B7CD311--