Math 100 6.1-8.3 have to show work.

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’s sales (in thousands of dollars) grow according to the recursive rule Pn=Pn-1 + 15, with initial population P0=40. a. Calculate P1 and P2 b. Find an explicit formula for Pn c. Use your formula to predict the store’s sales in 10 years d. When will the store’s sales exceed $100,000? 5. A population of beetles is growing according to a linear growth model. The initial population (week 0) was P0=3, and the population after 8 weeks is P8=67. 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’s 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 = 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 “golden”? 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, … 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 = 330 cps (typically denoted “E4”). If his sixth (thickest) string is to be two octaves lower, what is the frequency of the sixth string? 11. If A = 440 cps, the real “perfect fifth” would be E, whose frequency would be exactly 3/2 of A. What frequency is that? Compare that with the ‘tempered” 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 “A4” 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#, …) 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’s method to apportion the seats. b. If the legislature grows to 11 seats, use Hamilton’s 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’s 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’s 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)