19 Name: ____________________________________ 1. Your friend has a credit card with an APR of 49.9% ! What would his finance charge be on a $500 charge for just 1 month? 2. Your friend has 2 credit cards with balances that he cannot afford to pay off all at once. A $500 balance on a card with 15.99% APR and a $400 card with a %25.99. Calculate the monthly finance charges on each. What advice would you give your friend about paying off the balances on these cards? 1 Section 19 Name: ____________________________________ 3. With a beginning balance of $1200 and no additional charges during the next three months, you will just pay the minimum payment each month for the next three months. The APR is 24.99% and the minimum payment each month is 3% of the balance. Determine the finance charge, new balance, and minimum payment required for each of the next three months, and the starting balance for month 4 in the table below: Month 1 2 3 4 Starting balance $1200 Finance charge New balance Minimum payment a. b. c. d. e. What is the total of the minimum payments? What is the total of the finance charges? How much does the starting balance decrease after these three payments? The total of your finance charges is what percent of your total payments? Explain why making the minimum payment all the time is great for the credit card company, but not so great for the user. f. Explain why having a credit card and using it wisely is beneficial to you. 4. Create an Excel spreadsheet that can do the calculations for the credit card in #3 above. Using formulas and the drag function of Excel (see the notes), find the balance for month 12. (Yes, you need to do this- there is a link to submit this via Blackboard) 5. You open a credit card account and you charge $100 to the account on the first of each month to pay for your cable and internet subscription. You plan to pay just the minimum amount each month for this first 6 months until your summer job starts. The APR is 24.99% and the minimum payment is 3% of the balance. Fill in the table below: Mont Starting New Bal + Purch Finance New balance Minimum balance Purchases charge payment h 1 $0 $100 $100 2 $100 3 $100 4 $100 5 $100 6 $100 7 2 Section 19 Name: ____________________________________ 3 Section 20 Name: ____________________________________ Show all work including what values you plug into formulas in order to receive full credit. 1.) Bryan invests $500 in an account earning 4% interest that compounds annually. If he makes no additional deposits or withdraws, how much will be in the account: a. After 10 years? b. After 15 years? c. After 20 years? d. After 25 years? e. About how long would it take to double his $500 investment? 2.) Lori buys a $1500 certificate of deposit (CD) that earns 6% interest that compounds monthly. How much will the CD be worth in: a. 5 years? b. 10 years? c. 18 months? 4 Section 20 Name: ____________________________________ 3.) Lori gets an offer from another bank that is also paying 6% on CD's, but is compounding interest daily. How much will the $1500 CD be worth in: a. 5 years? b. 10 years? c. 18 months? 4.) You borrow $10,000 at 5% interest compounded weekly for tuition. While you do not have to make payments for the 5 years that you are in school, the interest is compounding every week. What is your loan balance after the 5 year grace period (if you've made no payments)? 5.) XXXX Create an Excel spreadsheet comparing simple and interest compounded yearly for an investment of $1200 over 30 years with an APR of 8%. XXXX a. Use the directions from class to create your spreadsheet showing both types of interest for all 30 years. b. Use the data from the spreadsheet to create a graphic (scatterplot) comparing the two types of interest. Write a paragraph making your comparisons and observations. 5 Section 20 Name: ____________________________________ 6.) Perry has an opportunity to put $12,000 into an investment with an APR of 5.25%. a. How long will it take his investment to double? _________________ b. How long will it take his investment to quadruple? _______________ 7.) The average population growth rate for whitetail deer is 0.35. Hunting laws are set to limit the time allowed for hunting deer with a goal of achieving about a 35% mortality rate on deer to keep the population in check. Years with a higher than 35% mortality will result in an overall decline in the deer population while years with a lower than 35% mortality rate will result in an increased population. a. If there were no hunting of whitetail deer allowed, how long would it take the population of deer to double?_______________________ to quadruple? ________________________________ b. If the growth rate exceeds the mortality rate, and the net effect were a 10% growth rate, how long would it take the population to double? ________________________ 8.) If the world's population growth rate continues to be 1.17%, how long before the population doubles? 6 Section 20 Name: ____________________________________ 9.) XXXX Research the population growth rate for the U.S. and estimate how long it will take the population to double at that rate. Write a short paragraph explaining your process and results. Check your results for reasonableness. XXXX 7 Section 21 Name: ______________________________ 1. Your classmate tells you the details of the great deal he got on his mortgage: 30-year 3.5% fixed rate with a 10% down payment. a. If his new home costs $136,000, what is his down payment? b. How much is he going to borrow to buy the house (assuming he only has the money to make the down payment from part a)? c. Use Excel's PMT function to determine how much his monthly payments would be. (Write the formula) d. If you put the correct formula in Excel you will get that his monthly payment is $549.63. How much will he pay in interest over the lifetime of this mortgage? 2. Bob Rohrman is offering a 2016 Toyota Camry for $29,000. If you have a $5,000 down payment and are able to borrow the rest at a 2.99% APR on a 48 month loan, how much will your payments be? (Write the formula) 8 Section 21 Name: ______________________________ 3. Suppose Calvin Cordozar Broadus, Jr. (aka Snoop Doggy Dogg) is considering moving his family to Manhattan. His real estate agent has managed to locate a penthouse apartment that overlooks Central Park for $2.4 million. He will have $2.1 million from the sale of his current home as a down payment. Snoop would like to finance the remainder of the cost and his banker has presented two options: a 30-year fixed-rate mortgage at 8% or a 20-year fixed-rate mortgage at 7.5%. a. How much will Snoop have to finance? b. Which loan is more economical in the long run? Use Excel to help determine your response. (Write the formulas) c. How much is saved in interest by choosing the more economical mortgage? 4. Your sister is considering the purchase of a home rather than renewing the lease on her twobedroom apartment. She is currently paying $850 per month for rent. She has asked you to help her decide what sort of home she might be able to afford if she wants to keep her living expenses the same. Her bank offers first-time home buyers (with good credit) a 30-year mortgage at a fixed rate of 5.49%. The cost of insurance and property taxes is about $175 per month in the neighborhood where she'd like to live. a. What monthly payment can she afford? b. Use Excel's PV function to determine what the most expensive mortgage she can afford would be. (Write the formula) 9 Section 21 Name: ______________________________ 5. Kanye and his wife, Kim, both work and have a combined gross income of $165,000 per year. They estimate the property taxes on their condo will be $2,100 and insurance would be about $1,500 per year. Kim has a car payment of $200 per month and they are both still paying off student loans for a combined total of $600 per month. a. Find out how much of a monthly mortgage Kanye and Kim can afford. See your notes for the total expense ratio calculation. b. Suppose the couple can get a 30 year loan with a rate of 3.5%, how large of a mortgage could they afford based on the payment you found in part a? 6. XXXX Excel: Complete the amortization table provided in the Excel document posted in Blackboard in the homework area by setting the appropriate values for a $100,000, 30-year mortgage at 6% interest and using Excel's autofill (drag) feature to fill in the cells to the end of the mortgage period. Use this to answer the following: a. How much of the first payment goes towards the Principal? Interest? b. How much of the last payment goes towards the Principal? Interest? c. Find the total interest paid by the end of the mortgage. d. How much will be owed on the mortgage after making payments for 10 years (hint this is 120 months)? e. How much is being paid in interest and principal at 10 years? f. How much interest has been paid on the mortgage at the end of 10 years? g. How many months will it take to pay at least half of the principal? 7. XXXX Change the spreadsheet from the last question so that the mortgage is for 15 years rather than 30 years. a. How much of the first payment goes towards the Principal? Interest? b. How much of the last payment goes towards the Principal? Interest? c. How much will be owed on the mortgage after making payments for 10 years (hint this is 120 months)? d. Find the total interest paid by the end of the mortgage. e. What are some advantages and disadvantages of getting a shorter term mortgage? 10 Section 21 Name: ______________________________ Excel Amortization table tips: Do enter the APR as a decimal value (Excel is formatted to then correctly represent it as a percentage). In order to correctly copy the month numbers in 'column A', you must select at least 2 consecutive months to establish a pattern to copy and drag. In 'column B' only drag cell 'B3' - do not select 'B2' as part of the drag and copy. 11 Section 22 Name: ____________________________________ Show all work including what values you plug into formulas in order to receive full credit. Explain the meaning of your answers using complete sentences when appropriate. 1. If a cell in an Excel spreadsheet uses the following formula to determine the future value of an investment: \"=FV(0.06/12, 12*6, 100.00)\" Note: You don't need Excel to answer this question. a. How much money is being invested each month? b. What is the APR? c. For how many years will monthly payments be made? d. How much money total will have been deposited into the account at the end of the deposits period? 12 Section 22 Name: ____________________________________ 2. If a cell in an Excel spreadsheet uses the following formula to determine the future value of an investment: \"=FV(0.0025, 360, 250)\" Note: You don't need Excel to answer this question. a. How much money is being invested each month? b. What is the APR? c. For how many years will monthly payments be made? d. How much money total will have been deposited into the account at the end of the deposits period? 13 Section 22 Name: ____________________________________ 3. John makes $2,800 per month and has an opportunity to invest $150 per month at an APR of 4.5% in a 401K plan through work. He plans to retire in 30 years. If income taxes are at 20% for him: a. Use Excel to determine how much his investment be worth in 30 years. i. Write the Excel formula that gives its future value _______________________________________________________ ii. Write the future value the formula gives: __$113,907.92__________ b. How much money will he deposit into the 401K over the 30 years? c. How much total interest will he earn on his 401K over the 30 years? d. How much will his monthly take-home pay decrease? Remember 401k investments are not taxed. e. How much tax savings is there over the 30 years? 14 Section 22 Name: ____________________________________ 4. Susie makes $1,900 per month and has an opportunity to save $100 per month at an APR of 3.25 in a 401K plan through work. She plans to retire in 40 years. If income taxes are at 20% for her: a. If Susie's company offered a 50% matching, use Excel to determine how much her investment be worth in 40 years. i. Write the Excel formula that gives its future value _________________________________________________________ ii. Write the future value the formula gives: __$147,481.17___________ b. How much would the company contribute to Susie's 401K over the 40 years? c. How much more is in the account when Susie retires than how much she deposited? 5. XXXX Pearl has an opportunity to save through her company's 401K retirement plan. Her company has a matching program whereby the company will contribute 50% of what the employee contributes or $200 per month whichever is the higher amount. The APR is 4.75%. Develop a strategy for Pearl by determining how much she should contribute monthly to the 401K so she will have at least $250,000 but not more than $300,000 after 25 years of monthly saving. 15 Section 22 Name: ____________________________________ 6. Sam plans to save $100 per month for the next 30 years to have a nest egg for retirement. Her sister Stevie has decided to wait and start saving $200 per month for half the time figuring she will do at least as well as her sister with this strategy. Explain why this is or is not a good strategy. Use an APR of 5%. 16 Section 23 Name: ____________________________________ Show all work and setups in order to receive full credit. Year CPI Tuitio n 2007 2008 2009 2010 2011 2012 2013 207.3 215.3 214.5 218.0 224.9 229.5 232.9 42 03 37 56 39 94 57 $91.3 $95.0 $99.6 $104. $107. $111. $116. 0 0 5 55 80 15 15 1. Above is a table of CPI and Ivy Tech tuition values. a. What is the absolute change in tuition from 2007 to 2015? 2014 236.7 36 $126. 15 2015 237.017 $133.15 b. Find the relative change in tuition from 2007 to 2015. c. Use your answers to a and b in a few meaningful sentences. 2. What is the absolute change in CPI from 2007 to 2015? a. Find the relative change in CPI from 2007 to 2015, and express your answer in a sentence. 17 Section 23 Name: ____________________________________ b. Which value, tuition or CPI, has had a higher relative change from 2007 to 2015? What can you conclude? 3. Students in a math 123 class have the following changes in their grades from Midterm to the final grade. Name Midterm Final absolute relative Jenny 62 70 Dave 72 81 Phil 95 89 Mary 62 58 a. Find the absolute and relative changes for these students. b.Who had the largest absolute increase in their grade? c. Who had the largest relative increase in their grade? d.Who had the largest absolute decrease in their grade? e. Who had the largest relative decrease in their grade? 4. Your friend's office is having a weight loss contest, the winner will get $100. The participants weights are in the table below: Name Start Finish absolute relative Jenny 145 lbs 120 lbs Dave 310 lbs 260 lbs Phil 230 lbs 180 lbs Mary 140 lbs 110 lbs a. Find the absolute and relative changes for the participants. 18 Section 23 Name: ____________________________________ b.Who do you believe should get the $100, explain why. 5. The fair market rental rate for Lafayette is $768 and for Kokomo is $704. a. Find the relative change from Lafayette to Kokomo. 19 Section 23 Name: ____________________________________ b. Write a sentence describing the difference between the two cities rent. c. Find the relative change from Kokomo to Lafayette. d. Write a sentence describing the difference between the two cities rent. 6. The fair market rental rate for Bloomington is $823 and for Kokomo is $704. a. Find the relative change from Bloomington to Kokomo. b. Write a sentence describing the difference between the two cities rent. 20 Section 23 Name: ____________________________________ c. Find the relative change from Kokomo to Bloomington d. Write a sentence describing the difference between the two cities rent. Smoking Rates 7. The CDC release the following report: \"Findings from the 2014 National Youth Tobacco Survey show that current ecigarette use (use on at least 1 day in the past 30 days) among high school students increased from 4.5 percent in 2013 to 13.4 percent in 2014\" a. What was the absolute change in e-cigarette use from 2013 to 2014? 21 Section 23 Name: ____________________________________ b. What was the relative change in e-cigarette use from 2013 to 2014? c. Use the value from parts a and b in a few sentences. 8. The CDC release the following report: \"Among high school students, current hookah use rose from 5.2 percent in 2013 (about 770,000 students) to 9.4 percent in 2014 (about 1.3 million students).\" a. What was the absolute change in hookah use from 2013 to 2014? b. What was the relative change in hookah use from 2013 to 2014? c. Use the values from parts a and b in a few sentences. Unemployment rates Year 2005 2006 2007 2008 Jan 5.3% 4.7% 4.6% 5.0% Feb 5.4% 4.8% 4.5% 4.9% Mar 5.2% 4.7% 4.4% 5.1% Apr 5.2% 4.7% 4.5% 5.0% May 5.1% 4.6% 4.4% 5.4% Jun 5.0% 4.6% 4.6% 5.6% Jul 5.0% 4.7% 4.7% 5.8% Aug 4.9% 4.7% 4.6% 6.1% Sep 5.0% 4.5% 4.7% 6.1% 2009 2010 2011 2012 7.8% 9.7% 9.1% 8.2% 8.3% 9.8% 9.0% 8.3% 8.7% 9.9% 9.0% 8.2% 9.0% 9.9% 9.1% 8.2% 9.4% 9.6% 9.0% 8.2% 9.5% 9.4% 9.1% 8.2% 9.5% 9.5% 9.0% 8.2% 9.6% 9.5% 9.0% 8.1% 9.8% 9.5% 9.0% 7.8% 22 Oct 5.0% 4.4% 4.7% 6.5% 10.0 % 9.5% 8.8% 7.8% Nov 5.0% 4.5% 4.7% 6.8% Dec 4.9% 4.4% 5.0% 7.3% 9.9% 9.8% 8.6% 7.8% 9.9% 9.4% 8.5% 7.9% Section 23 2013 2014 2015 2016 Name: ____________________________________ 7.9% 6.6% 5.7% 4.9% 7.7% 6.7% 5.5% 4.9% 7.5% 6.6% 5.5% 5.0% 7.5% 6.2% 5.4% 5.0% 7.5% 6.3% 5.5% 4.7% 7.5% 6.1% 5.3% 7.3% 6.2% 5.3% 7.2% 6.1% 5.1% 7.2% 5.9% 5.1% 7.2% 5.7% 5.0% 7.0% 5.8% 5.0% 6.7% 5.6% 5.0% http://data.bls.gov/timeseries/LNS14000000 9. The table above represents the monthly unemployment rates in the US from January of 2005 through May of 2016. a. Find the absolute change in unemployment from December 2005 to December of 2010. b. Find the relative change in unemployment from December 2005 to December of 2010. c. Use the value from parts a and b in a sentence(s). 10. Consider the unemployment rate data for 2009. a. Find the absolute change in the unemployment rate during 2009 (i.e. from Jan 2009 to Dec 2009). b. Find the relative change in the unemployment rate during 2009. 23 Section 23 Name: ____________________________________ c. Write a few sentences reporting on the unemployment rate for 2009 using your values from parts a and b. 11. Consider the unemployment rate in 2015. a. Find the absolute change in the unemployment rate during 2015 (i.e. from Jan 2015 to Dec 2015). b. Find the relative change in the unemployment rate during 2015. c. Write a few sentences reporting on the unemployment rate for 2015 using your values from parts a and b. 12. Suppose the absolute change in the unemployment rate in from January 2015 to the end of 2015 were the same as the absolute change for 2009, what would the effect on the unemployment rate have been in December 2015? 24 Section 23 Name: ____________________________________ 13. An economist predicts the unemployment rate will increase 12%. Is this value most likely a relative increase or an absolute increase? Use values from the table and the values you found above to support your answer. 25 Section 24 Name: ____________________________________ 1. Sales tax in Indiana is 7%, if a t-shirt is sold for $5, how much will you pay total. 2. You are charged $7.33 total for a meal, assume the 7% sales tax, how much was the menu price of this item? 3. A book is marked 20% off. a. What percent of the original price is the sales price? b. If the original price is $55, how much will the sales price be? c. If the sales price rings up as $57.60, what was the original price? 4. Gas prices are up 12% this month. a. This means that the current price is what percent of last month's price? 26 Section 24 Name: ____________________________________ b. If prices at one station were $3.20 last month, what are price now? c. If prices are $3.80 in Lafayette this month, what were they last month? 5. Indiana's population has increased by 9.5% since 2000, when it was about 6 million people, what is Indiana's population now? 6. An item that normally sells for $130 is marked down by 30%. What is the sale price? 7. You got a great deal on a new computer for $800 that was marked down by 60% from the original price. What was the original price? 27 Section 24 Name: ____________________________________ 8. Your take home pay is $1500 and you have 22% withheld in taxes. What is your gross pay? 9. You plan to leave a 15% tip and your dinner bill is $45 (tax included). How much total should you leave? 10. You paid $6.99 for a shirt that was 75% off, what was the original price of the shirt? 11. You are charged $279 on your credit card for a hotel stay, you call to complain about the unexpectedly high charge, but are told there are a total of 24% taxes for hotel rooms where you stayed. What was the advertised price of the room before taxes? 28 Section 24 Name: ____________________________________ 12. You are charged $16.05 after tax for a meal. Assume sales tax is 7%, what was the menu price for the meal? 13. 20% of city employees ride the bus to work. This is up 10% from last year. What percent of employees rode the bus to work last year? 14. The portion of students taking summer classes decreased 6.3% from 2015 to 2016. If 38% of students took summer classes in 2015, what portion were taking summer classes in 2016? 15. The interest rate on a car loan has increased 50% over the last 10 years and is now 9%. What was the rate 10 years ago? 29 Section 24 Name: ____________________________________ 16. The amount of working students had a relative increase of 10% and is now 77%, what was the amount previous to the increase? 17. If you earn $1200 per month and you expect your earnings to increase by 10% per year, how much do you think you will be making in 5 years? Explain. 30 Section 25 Name: ____________________________________ Show all work and setups in order to receive full credit. 1. A tree increases in diameter each year by an average of 0.51cm. If the tree currently has a diameter of 4 inches, how old do you estimate the tree is? 2. If rain is falling at a rate of inch per hour, how much rain would you expect after 6 hours? 31 Section 25 Name: ____________________________________ 3. Consider the variation of temperature with altitude depicted in the graph below. Variation of temperature (F) with altitude Temperature 62.0 60.0 58.0 56.0 54.0 52.0 50.0 48.0 46.0 44.0 42.0 40.0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 altitude (feet above sea level) a. What is the dependent variable? b. What is the independent variable? c. What is the \"y-intercept\"? d. What is the slope? e. Write a sentence to explain what the slope means. f. Use your answers to construct an equation for the linear model, y = mx + b, that describes the graph. g. Use your model to predict what the temperature would be at 7000 feet above sea level. 32 Section 25 Name: ____________________________________ 4. The fair market rental rate for Columbus was $730 in 2013 and $551 in 2003. Find and interpret the rate of change for rent in Columbus during this period. 5. The environment club has saved 200 pounds of cans and promises to collect 20 pounds of cans each week and will use the profits to buy additional recycling bins. Construct a linear model for their collection program. a. What will the independent variable, x, represent? b. What will the dependent variable, y, represent? c. What is the starting value, b, for this model? d. What is the slope, m, for this model? e. Write the model in y = mx + b form. f. How many pounds of cans will the club have by week 12? g. When will the club have 320 pounds of cans? 33 Section 25 Name: ____________________________________ 6. The psychology club is having a self-proclaimed psychic come to their campus fundraising event to demonstrate his abilities. He charges $200 for these events, and the club is charging $1.50 for tickets with a chance to have the psychic read the ticket holder's mind. a. Let x represent the number of tickets sold and y represent money in a linear model which can be used to estimate the profit or loss based upon the number of tickets sold. b. How much would the club gain or lose by selling 125 tickets? c. How many tickets are needed to break even? 7. The cost of a LCD TV dropped from $265 in 2012 to $199 in 2014. a. Find the rate at which the cost has been decreasing. b. Construct a linear model to estimate future costs of TV's c. Use your model to estimate what the cost will be in 2016. 34 Section 25 Name: ____________________________________ 8. Online jewelry sales have increased steadily over the last 10 years. In 2003, sales were approximately 2 billion dollars, and in 2010 they were approximately 10 billion. a. Find the rate at which online jewelry sales have been increasing. b. Construct a linear model which can be used to estimate jewelry sales. c. Use your model to estimate online jewelry sales for 2014. 9. In 1963, postage was 5 cents per ounce. In 1981, postage was 18 cents per ounce. a. Establish a linear model which can be used to estimate the postage per ounce based upon the year (or you can use the number of years since 1963.) b. If the trend had continued through to today, what would the postage per ounce be? 35 Section 25 Name: ____________________________________ 10. Actual price of postage today is 46 cents for the first ounce and 20 cents for each additional ounce. a. Construct a linear model which can be used to estimate cost of postage. b. Use your model to estimate the postage of a package which weighs 250 grams. c. If you are willing to spend no more than three dollars on postage for a package, what is the most a package can weigh that you could send on budget? 36 Section 25 Name: ____________________________________ 11. XXXX Below is an excerpt from an IU Bloomington Health article. a. Use information from the article to establish a linear model for the percentage of high school seniors that said they had 'used alcohol at least once in their lifetime' when given year since 1993. b. Use the model to estimate the percentage that would say yes in 2016. c. Discuss the assumptions made by the model and the reasonableness of the model. d. Could you use this to estimate the suicide rate for this group of people in the year 2050? Why or why not? IUB Newsroom 24th annual survey of Indiana children and teens shows 21-year decline in alcohol use Fewer Hoosier students depressed than national average, finds survey by the IU School of Public Health-Bloomington's Indiana Prevention Resource Center Sept. 23, 2014 FOR IMMEDIATE RELEASE BLOOMINGTON, Ind. -- The 24th Annual Survey of Alcohol, Tobacco and Other Drug Use by Indiana Children and Adolescents, conducted by the Indiana Prevention Resource Center at Indiana University's School of Public Health-Bloomington, highlights a 21-year decline in the lifetime and monthly use of alcohol across all grade levels (6-12). "We are extremely pleased to see fewer youth using alcohol," Indiana Prevention Resource Center executive director Ruth Gassman said. "Prevention education and efforts to reduce access to alcohol in homes and stores are having a positive effect. We're also seeing success in community groups working to change the view that alcohol consumption by youth is harmless." In 1993, more than 80 percent of high school seniors had tried alcohol at least once in their lifetime. By 2014, fewer than 60 percent of seniors had done so. In 1993, more than 50 percent of high school seniors were drinking alcohol at least once a month. By 2014, only about 30 percent of seniors were drinking alcohol every month. Indiana students reported in 2014 that their most common means of acquiring alcohol was not through stores or restaurants (0.2 percent and 0.5 percent for 12th-graders) but from having another person purchase it for them or give it to them, or from a family member. 37 Section 25 Name: ____________________________________ Store and restaurant sales are regulated, and stricter enforcement of sales and server laws reduce the chances of youth making purchases or being served. The 2014 survey results are based on responses from 119,147 students in Grades 6 through 12 at 429 public and private schools in Indiana. 38 Section 26 Name: ____________________________________ Show work to receive full credit. Make sure to show the values you put into the linear models. 1. Vehicle Registrations Vehicle Registrations in the United States, 1925-2011 300 250 200 Registrations (in millions) f(x) = 3.02x - 5819.5 R = 0.97 150 100 50 0 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 Year Use the above scatter plot to answer the following questions: a. What is the independent variable and what does it represent? b. What is the range of the independent variable? c. What is the dependent variable and what does it represent? d. State the trend line (regression line). 39 Section 26 Name: ____________________________________ e. Write a sentence explaining the value of the slope for this regression line. f. Use the R2 value to determine the r value. Is this a reasonable model for the data? Why or why not? g. Consider the model/regression line. i. How would you use the model to predict the registration for 2005? Note the range of the x-value. ii. What value does the model predict for the number of registrations in 2005? iii. How does this compare to the actual value of 241 million? 40 Section 26 Name: ____________________________________ h. What value does the model predict for the number of registrations in 2020? i. Is it reasonable to use the model to make predictions for 2020? Explain your answer. 2. Atmospheric Carbon Dioxide Concentration 1970-2012 400.00 380.00 f(x) = 1.62x - 2864.6 R = 0.99 391.63 360.00 CO2 in ppm 340.00 320.00 300.00 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 Year a. What is the independent variable and what does it represent? b. What is the dependent variable and what does it represent? c. Describe the relationship/trend between the two variables in this graph. 41 Section 26 Name: ____________________________________ d. Write a sentence explaining the value of the slope for this regression line. e. Use the R2 value to determine the r value. Is this a reasonable model for the data? Why or why not? f. Use the equation to estimate the CO2 level in 2011. How does it compare to the actual value labeled in the graphic? US coal consumption 1950-2014 3. XXXX In Blackboard, you will find an Excel spreadsheet of the US coal consumption data. Along with the years 1950-2014, you will find coal consumption by 'quadrillion BTU' and by 'million tons of oil equivalent' in the spreadsheet. Use the data for one of these measures of coal consumption to perform the following tasks: a. Create a scatter plot of the data. b. Include a title for the scatter plot and labels for both the horizontal and vertical axes. c. Add the trend line and R2 to the graph. d. Create a two-paragraph report with your graph (showing the trend line and R2) addressing the following items: 42 Section 26 Name: ____________________________________ i. Does the R2 indicate correlation between your variables? ii. Interpret the slope in a complete sentence. iii. Use the trend line equation to estimate the coal consumption for 2014, and compare this estimate to the actual consumption. iv. Use the trend line to estimate the coal consumption from your birth year. Compare that estimate to the actual 2014. How much has coal consumption changed since your birth year? What is the relative change in coal consumption since your birth year? 43 Section 26 Name: ____________________________________ 4. XXXX World Solar-Generated Electricity In Blackboard, you will find an Excel spreadsheet, World Solar-generated Electricity, 1990-2013, with the following data to analyze the world wind power over these 22 years. Cumulative Installed Offshore Wind Power Capacity in Megawatts by year: NOTE: Data can be retrieved from the following website. Look for World Cumulative Installed Offshore Wind Power Capacity and Net Annual Addition, 1991-2012 XLS file. http://www.earthpolicy.org/data_center/C23 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 0.4 0.5 0.5 0.6 0.6 0.6 0.7 0.7 0.8 0.9 1.0 1.3 1.6 2.0 2.6 3.7 5.0 6.7 11.2 19.1 30.5 59.2 94.1 124.8 Use the data to perform the following tasks: a. Create a scatter plot of the data. b. Include a title for the scatter plot and labels for both the horizontal and vertical axes. c. Add the trend, and display the trendline equation and R2 value on the graph d. Create a two-paragraph report with your graph (showing the trend line and R2) addressing the following items: i. Does the R2 indicate correlation between your variables? ii. Interpret the slope in a complete sentence. iii. Use the trend line to estimate the cumulative world solar power for 2012 iv. Use the trend line to estimate the cumulative world wind power for 2022. v. Is it reasonable to predict that far into the future (2022)? Why or why not? 44 Section 27 Name: ____________________________________ Show work in order to receive full credit. 1. Researchers find that there are 60 Raccoons on an island. When they return a year later, they find that there are 84. Assuming an exponential growth pattern, what is the annual population growth rate for the raccoons? 2. Your friend sends out a chain letter e-mail to 12 people by the next day 15 people have received the letter. Assuming an exponential growth pattern, what is the daily growth rate for the number chain letters received? 3. An arborist creates a table of different tree height patterns over a 4 year period. Which of the trees has an exponential growth pattern? Why? Time Yew Willow 0 1 2 3 2 3.5 5 6.5 4 6 9 13.5 Mulberr y 2 4 6 10 45 Section 27 Name: ____________________________________ 4. Consider the data in the table. Time Value Absolute Change Relative Change 0 13.60 1 14.85 2 16.10 3 17.35 4 18.60 5 19.85 a. Complete the table by computing the absolute and relative change. b. Which model would better represent this data, linear or exponential? Write a meaningful sentence to explain your answer. c. Find the model for this data. d. What value does your model predict when time is 8? 46 Section 27 Name: ____________________________________ 5. Consider the data in the table. Time Value Absolute Change Relative Change 0 13.60 1 17.00 2 21.25 3 26.56 4 33.20 5 41.50 a. Complete the table by computing the absolute and relative change. b. Which model would better represent this data, linear or exponential? Write a meaningful sentence to explain your answer. c. Find the model for this data. d. What value does your model predict when time is 8? 47 Section 27 Name: ____________________________________ 6. According to the 2010 United States Census, the population of Lafayette was 67,140, roughly a 19% increase from 56,397 in 2000. a. Construct an exponential model for Lafayette's population. b. Use your model to predict Lafayette's population in 2020. 7. Frogs - A species of frog's population grows 24% every year. Suppose 100 frogs are released into a pond. a. Construct an exponential model for this population. b. How many frogs will there be in 5 years? c. How many frogs will there be in 10 years? d. About when will there be 1000 frogs? 48 Section 27 Name: ____________________________________ 8. Pandas - There is a well-studied Panda population in Wuyipeng. In 1981 there were 25 Panda's and the researchers determined they had an annual population growth of 1.066. www.bearbiology.com a. Construct an exponential model for this population. b. Assuming no deaths, how many Panda's would the researchers expect by 2001? 9. XXXX Create your own population model Task #1) What is the name of your species/animal? Task #2) At this point in time (today), what is the total population of your species? Task #3) Pick a number between 5 and 80 to be the percent of growth: Percent growth = ____% every month Task #4) Write an equation that models the exponential growth of this species Population = Task #5) Determine what will be the population of your species in 1 month:___________ 6 months:___________ 2 months:___________ 1 year:___________ Task #6) Graph this exponential growth equation 14 12 10 8 6 4 2 0 1 2 3 4 5 6 7 8 9 49 10 11 12 Section 27 Name: ____________________________________ 10. Bacteria such as Staphylococcus and Salmonella are notorious for spoiling food and making us sick if ingested. http://www.whitsunday.qld.gov.au/food What if a single bacterium landed in a nutrient filled test tube at 10:00 am? Since bacteria use nutrients and reproduce by doubling (binary fission), at 10:01 am there are 2 bacteria. Now the binary fission continues and at 10:02 there are 4 bacteria, and 10:03 there are 8 bacteria and so on. In other words, the bacteria consume the nutrients present and double every minute. By 11:00 am the test tube is full. Now since there are no longer nutrients present, the bacteria begin to die. a. How many bacteria are in the test tube at 10:06 am? b. How many bacteria are in the test tube at 10:20 am? c. How many bacteria are in the test tube at 10:50 am? d. If the test tube is full at 11:00 am, what fraction of the test tube was full at 10:59 am? e. What fraction of the tube was full at 10:58? 50 Section 27 Name: ____________________________________ 11. XXXX Invasive Plants - Excel Kudzu is an invasive plant that can spread rapidly if not kept in check. Suppose that kudzu is known to spread 20% per year in a certain area. Suppose you start with an infestation of 0.5 acres. a. Use Excel to make a table of values of the area that will be covered over a ten year period. b. When will the size reach 2 acres? c. Write an equation to represent the size of the infestation for a given year. d. Kudzu will grow even faster if there is an increase in the supply of CO2. Answer questions (a)-(c) above if the conditions are such that now the growth rate is 40%. e. Did doubling the growth rate double the size of the infestation for the value at year ten? Explain. 51 Section 28 Name: ____________________________________ Show all work and setups in order to receive full credit. 1. The half-life of a radioactive substance is one day, meaning that every day half of the substance has decayed. Suppose you have 100 grams of this substance. a. Construct an exponential model for the amount of the substance remaining on a given day. b. How much of the substance would be left after a week? 2. Suppose a tortoise is 2000 feet from the ocean. Each day the tortoise travels one-half of the remaining distance to the ocean. Use this information to: a. Construct a model that represents the remaining distance that the tortoise must travel to reach the ocean. b. Compute the remaining distance to the ocean after 4 days of travel. 52 Section 28 Name: ____________________________________ 3. A certain vehicle loses 35% of its value each year. a. If the vehicle has an initial value of $25,000, construct a model that represents the value after x years. b. Compute the value of the vehicle at the end of the 3rd year. 4. Atmospheric pressure decreases by about 12% for every 1000 meters you climb. The pressure at sea level is about 1013 atmospheres. a. Construct a model to represent the atmospheric pressure at a given altitude in thousands of meters. b. How many atmospheres of pressure will you feel at 5,895meters? (Top of Mt. Kilimanjaro) c. How many atmospheres of pressure will you feel at 8,848 meters? (Top of Mt. Everest) 53 Section 28 Name: ____________________________________ d. How many atmospheres of pressure will you feel at 383 meters? (highest point in Indiana) 5. XXXX Coffee withdrawal is now considered an actual diagnosis. Some people have become dependent on caffeine and drink caffeine-rich beverages on a regular basis to keep these levels somewhat constant. If the milligrams of caffeine in the body drop too low, it is possible to suffer from withdrawal symptoms. Let's take a look at two different people: Annie drinks a 16 oz. can of energy drink before she works out in the morning. Ryan drinks a 16 oz. cup of brewed coffee before going to class in the morning, where he primarily sits and listens to lectures. We know: 1 cup (16 oz.) of brewed coffee contains 100 mg of caffeine and 1 can (16 oz.) of energy drink contains 160 mg of caffeine. 54 Section 28 Name: ____________________________________ a. If Ryan metabolizes the caffeine at a rate of 25% per hour, when will he likely begin to feel the effects of caffeine withdrawal? Explain. b. If Annie's workout causes her to metabolize the caffeine at triple the rate of Ryan, when will she likely begin to feel the effects of caffeine withdrawal? Explain. c. Provide the equation to represent the caffeine levels in the body for each person at any hour past the initial drink. d. Make an Excel table displaying the caffeine levels for each person for a 12 hour period assuming they would not have had an additional cup of coffee or other source of caffeine. e. Use Excel to make a line graph and compare both Ryan's and Annie's caffeine levels. f. Write a paragraph comparing the two graphs. When does the caffeine leave each person's system? 55 charlesmunyi8@gmail.com