Student need urgent help for this Maths 123 homework.

Show all work. Make sure to show what values you used in any formulas.

• You have to charge $500 of car repairs and no additional charges during the next two months, you will just pay the minimum payment each month for the next two months. The Annual Percentage Rate (APR) is 15.99% and the minimum payment each month is 4% of the balance. Determine the finance charge, new balance, and minimum payment required for each of the next two months, and the starting balance for month 3 in the table below:

Month	Starting balance	Finance charge	New balance	Minimum payment
1	$500
2
3

• Find the balance on an account if you invest $100 at 5% for 10 years compounded annually.

• Find the balance on an account if you invest $100 at 5% for 10 years compounded monthly.

A business finds that it has to increase its staff by 5% each year due to growth. After how many years would the size of their staff double?Your friend purchases a $165,000 house.Your friend is able to invest $150 a month in a 401(k) with a predicted growth rate of 3% over 20 years. What would you type into Excel to find the predicted value in his 401(k)?The Poverty Rate for Knox County in 2011 is ___________ percent more than the Poverty Rate of Dubois County in 2011. (See page 3 for the chart)

Percent of All Ages in Poverty
State / County Name	2001	2011
United States	11.7	15.9
Indiana	9	15.8
Dubois County	5	8.3
Elkhart County	9	18.3
Knox County	13.2	19.7
Tippecanoe County	10.5	21.4
Wayne County	11	21.1

• Find the Absolute Change in the Percent of those living in Poverty for the state of Indiana from 2001 to 2011.
• Find the Relative Change in the Percent of those living in Poverty for the state of Indiana from 2001 to 2011.
• Use the Relative Change you found in 9 to write a sentence explaining the change.
• You are charged $13.21 total for a meal, assume the 7% sales tax, how much was the menu price of this item?
• An item that normally sells for $220 is marked down by 40%. What is the sale price?
• You plan to leave a 15% tip and your dinner bill is $32. How much tip money should you give?
• If gas prices are now $3.95 and they were up 8% from 6 months ago, how much were gas prices 6 months ago?
• According to the Ivy Tech website, students will pay a $60 technology fee and $121.50 per credit hour for Spring 2014.
• Set up a linear model to calculate a students bill based on this information.

• The independent variable in my model is ____ and it represents______________
• The dependent variable in my model is ____ and it represents_______________
• Use your model to determine how many credit hours a student is taking if his bill is $1639.50?
• You invest $230 to start a sandwich stand and decide to charge $4.25 per sandwich.
• Set up a Linear Model that determines your profit or loss based on the number of sandwiches.

How many sandwiches must you sell to break even?How many sandwiches must you sell to make a $100 profit?

• The median adjusted income in Indiana in 1990 was $46,300 and in 2011 was $44,450. Find and interpret the average rate of change.

• A can of soda in 1972 costs $0.10, by 2012 it cost $1.25.
• Construct a linear model that can be used to predict the cost of soda in a given year.

• Use your linear model to predict the cost of a soda in 2014.

A scatter plot was made using data on tuition at Public 2 year colleges from 1964-2011 and a linear trend line was added. The equation and R² for the trendline are in the textbox on the graphic. Data from: http:/ces.ed.gov/fastfacts/display.asp?Use the linear model for the trend line to predict tuition costs for 2014.

• Find the r value for this regression line. What does it tell you?

Should you use the linear model to predict tuition for 2025? Why or Why not?A scatterplot was made using the annual CPI rate from 1960 to 2014 and a trend line was added.

• What is the independent variable in this model, what does it represent?
• What is the dependent variable in this model, what does it represent?
• Use the trend line equation to estimate the CPI for 2000.
• What can be said about the accuracy of this model?
• Interpret the meaning of the slope of the trend line.
• Should we use this model to predict CPI for 2020? Why or Why not?

To celebrate Ivy Techs anniversary, a landscaper puts 50 water lilies on a pond the week before classes start. Unfortunately, every lily splits and produces a second lily once a week. Fill out this table for the number of lilies for the first few weeks: Write an equation to find the number of lilies in a given week.

• How many lilies will be on the pond by week 16?

• The landscaper pours 200 gallons of herbicide in the pond.
• If the herbicide degrades 10% each week, how much will be in the pond after 1 week passes?

Write an equation to find the amount of herbicide in any given week.Construct an exponential model for this population.

How many beetles will there be in 10 years?

How many beetles will there be in 20 years?

About when will there be 100,000 beetles?

• Show all work. Make sure to show whatvalues you used in any formulas.

  1) You have to charge $500 of car repairs and noadditional charges during the next two months, you will just pay the minimumpayment each month for the next two months.The Annual Percentage Rate (APR) is 15.99% and the minimum paymenteach month is 4% of the balance.Determine the finance charge, new balance, and minimum payment required for each of the next two months, andthe starting balance for month 3 in the table below:

  Month	Starting balance	Finance charge	New balance	Minimum payment
  1	$500
  2
  3

  2) Find the balance on an account if youinvest $100 at 5% for 10 years compounded annually.

  3) Find the balance on an account if youinvest $100 at 5% for 10 years compounded monthly.

  4) A business finds that it has toincrease its staff by 5% each year due to growth. After how many years wouldthe size of their staff double?

  5) Your friend purchases a $165,000house.

  a. If he makes a 20% down payment, howmuch money will he borrow for his mortgage?

  b. The bank is willing to give him thismortgage on a 30 year loan with a 4% APR, what would you enter into Excel in order to find out his monthlypayment?

  c. Excel would return a value of $630.19.How much interest will your friend pay over 30 years of his loan?

  6) Your friend is able to invest $150 amonth in a 401(k) with a predicted growth rate of 3% over 20 years. What wouldyou type into Excel to find the predicted value in his 401(k)?

  7) The Poverty Rate for Knox County in 2011 is___________ percent more than the Poverty Rate of Dubois County in 2011. (See page 3 for the chart)

  Percent of All Ages in Poverty
  State / County Name	2001	2011
  United States	11.7	15.9
  Indiana	9	15.8
  Dubois County	5	8.3
  Elkhart County	9	18.3
  Knox County	13.2	19.7
  Tippecanoe County	10.5	21.4
  Wayne County	11	21.1

  8) Find the Absolute Change in the Percent ofthose living in Poverty for the state of Indiana from 2001 to 2011.

  9) Find the Relative Change in the Percent ofthose living in Poverty for the state of Indiana from 2001 to 2011.

  10) Use the Relative Change you found in 9 towrite a sentence explaining the change.

  11) You are charged $13.21 total for a meal,assume the 7% sales tax, how much was the menu price of this item?

  12) An item that normally sells for $220 is markeddown by 40%. What is the sale price?

  13) You plan to leave a 15% tip and your dinnerbill is $32. How much tip money shouldyou give?

  14) If gas prices are now $3.95 and they were up8% from 6 months ago, how much were gas prices 6 months ago?

  15) According to the Ivy Tech website,students will pay a $60 technology fee and $121.50 per credit hour for Spring2014.

  a. Set up a linear model to calculate astudents bill based on this information.

  b. The independent variable in my modelis ____ and it represents______________

  c. The dependent variable in my model is____ and it represents_______________

  d. Use your model to determine how manycredit hours a student is taking if his bill is $1639.50?

  16) You invest $230 to start asandwich stand and decide to charge $4.25 per sandwich.

  a. Set up a Linear Model thatdetermines your profit or loss based on the number of sandwiches.

  b. How many sandwiches must yousell to break even?

  c. How many sandwiches must yousell to make a $100 profit?

  17) The median adjusted incomein Indiana in 1990 was $46,300 and in 2011 was $44,450. Find and interpret theaverage rate of change.

  18) A can of soda in 1972 costs$0.10, by 2012 it cost $1.25.

  a. Construct a linear modelthat can be used to predict the cost of soda in a given year.

  b.Use your linear model to predict the cost of a soda in 2014.

  19)A scatter plot was made using data on tuition atPublic 2 year colleges from 1964-2011 and a linear trend line was added. Theequation and R² for the trendline are in the textbox on the graphic.Data from: http:/ces.ed.gov/fastfacts/display.asp?id=76

  a.Use the linear model for the trend line topredict tuition costs for 2014.

  b. Findthe r value for this regression line. What does it tell you?

  c.Should you use the linear model to predicttuition for 2025? Why or Why not?

  20)A scatterplot was made using the annual CPI ratefrom 1960 to 2014 and a trend line was added.

  a.What is the independent variable in this model,what does it represent?

  b.What is the dependent variable in this model,what does it represent?

  c. Use the trend line equation to estimate the CPI for 2000.

  d. What can be said about theaccuracy of this model?

  e. Interpret the meaning of theslope of the trend line.

  f.Should we use this model to predict CPI for 2020? Why or Whynot?

  21)To celebrate Ivy Techs anniversary, a landscaperputs 50 water lilies on a pond the week before classes start. Unfortunately,every lily splits and produces a second lily once a week.

  a.Fill out this table for the number of lilies forthe first few weeks:

  Week 0	50
  Week 1
  Week 2
  Week 3
  Week 4

  b.Write an equation to find the number of liliesin a given week.

  c.How many lilies will be on the pond by week 16?

  22)The landscaper pours 200 gallons of herbicide inthe pond.

  a.If the herbicide degrades 10% each week, howmuch will be in the pond after 1 week passes?

  b.Write an equation to find the amount ofherbicide in any given week.

  c.The landscaper will put another dose in the pondwhen the herbicide level reaches 50 gallons. In about how many weeks will heneed to add more herbicide?

  23) Beetles A species of beetlespopulation grows 32% every year. Suppose 100 beetles are released into a field.

  a. Constructan exponential model for this population.

  b. Howmany beetles will there be in 10 years?

  c.How many beetles will there be in 20 years?

  d.About when will there be 100,000 beetles?

UNIT 3 Due: ____________ Name: ________________________________ Show all work. Make sure to show what values you used in any formulas. 1) You have to charge $500 of car repairs and no additional charges during the next two months, you will just pay the minimum payment each month for the next two months. The Annual Percentage Rate (APR) is 15.99% and the minimum payment each month is 4% of the balance. Determine the finance charge, new balance, and minimum payment required for each of the next two months, and the starting balance for month 3 in the table below: Month Starting balance 1 $500 2 3 Finance charge New balance Minimum payment 2) Find the balance on an account if you invest $100 at 5% for 10 years compounded annually. 3) Find the balance on an account if you invest $100 at 5% for 10 years compounded monthly. 4) A business finds that it has to increase its staff by 5% each year due to growth. After how many years would the size of their staff double? 5) Your friend purchases a $165,000 house. a. If he makes a 20% down payment, how much money will he borrow for his mortgage? 1 UNIT 3 Due: ____________ Name: ________________________________ b. The bank is willing to give him this mortgage on a 30 year loan with a 4% APR, what would you enter into Excel in order to find out his monthly payment? c. Excel would return a value of $630.19. How much interest will your friend pay over 30 years of his loan? 6) Your friend is able to invest $150 a month in a 401(k) with a predicted growth rate of 3% over 20 years. What would you type into Excel to find the predicted value in his 401(k)? 7) The Poverty Rate for Knox County in 2011 is ___________ percent more than the Poverty Rate of Dubois County in 2011. (See page 3 for the chart) Percent of All Ages in Poverty State / County Name 200 1 United States 11.7 Indiana 9 2011 15.9 15.8 2 UNIT 3 Due: ____________ Dubois County Elkhart County Knox County Tippecanoe County Wayne County 5 9 13.2 10.5 11 Name: ________________________________ 8.3 18.3 19.7 21.4 21.1 8) Find the Absolute Change in the Percent of those living in Poverty for the state of Indiana from 2001 to 2011. 9) Find the Relative Change in the Percent of those living in Poverty for the state of Indiana from 2001 to 2011. 10) Use the Relative Change you found in 9 to write a sentence explaining the change. 11) You are charged $13.21 total for a meal, assume the 7% sales tax, how much was the menu price of this item? 12) An item that normally sells for $220 is marked down by 40%. What is the sale price? 3 UNIT 3 Due: ____________ Name: ________________________________ 13) You plan to leave a 15% tip and your dinner bill is $32. How much tip money should you give? 14) If gas prices are now $3.95 and they were up 8% from 6 months ago, how much were gas prices 6 months ago? 15) According to the Ivy Tech website, students will pay a $60 technology fee and $121.50 per credit hour for Spring 2014. a. Set up a linear model to calculate a student's bill based on this information. b. The independent variable in my model is ____ and it represents______________ c. The dependent variable in my model is ____ and it represents_______________ d. Use your model to determine how many credit hours a student is taking if his bill is $1639.50? 16) You invest $230 to start a sandwich stand and decide to charge $4.25 per sandwich. a. Set up a Linear Model that determines your profit or loss based on the number of sandwiches. b. How many sandwiches must you sell to break even? 4 UNIT 3 Due: ____________ Name: ________________________________ c. How many sandwiches must you sell to make a $100 profit? 17) The median adjusted income in Indiana in 1990 was $46,300 and in 2011 was $44,450. Find and interpret the average rate of change. 18) A can of soda in 1972 costs $0.10, by 2012 it cost $1.25. a. Construct a linear model that can be used to predict the cost of soda in a given year. b. Use your linear model to predict the cost of a soda in 2014. 19) A scatter plot was made using data on tuition at Public 2 year colleges from 1964-2011 and a linear trend line was added. The equation and R 2 for the trendline are in the textbox on the graphic. Data from: http:/ces.ed.gov/fastfacts/display.asp?id=76 5 UNIT 3 Due: ____________ Name: ________________________________ Average 2 yr College Tuition 8,500 8,000 7,500 7,000 6,500 f(x) = 50.24x - 93935.1 R = 0.74 Dollars 6,000 5,500 5,000 4,500 4,000 1964 1974 1984 1994 2004 a. Use the linear model for the trend line to predict tuition costs for 2014. b. Find the r value for this regression line. What does it tell you? c. Should you use the linear model to predict tuition for 2025? Why or Why not? 6 UNIT 3 Due: ____________ Name: ________________________________ Annual CPI 250.0 200.0 f(x) = 4.24x - 8315.16 R = 0.98 150.0 100.0 50.0 0.0 1960 1970 1980 1990 2000 2010 20) A scatterplot was made using the annual CPI rate from 1960 to 2014 and a trend line was added. a. What is the independent variable in this model, what does it represent? b. What is the dependent variable in this model, what does it represent? c. Use the trend line equation to estimate the CPI for 2000. d. What can be said about the accuracy of this model? e. Interpret the meaning of the slope of the trend line. f. Should we use this model to predict CPI for 2020? Why or Why not? 7 UNIT 3 Due: ____________ Name: ________________________________ 21) To celebrate Ivy Tech's anniversary, a landscaper puts 50 water lilies on a pond the week before classes start. Unfortunately, every lily splits and produces a second lily once a week. a. Fill out this table for the number of lilies for the first few weeks: Week 0 Week 1 Week 2 Week 3 Week 4 50 b. Write an equation to find the number of lilies in a given week. c. How many lilies will be on the pond by week 16? 22) The landscaper pours 200 gallons of herbicide in the pond. a. If the herbicide degrades 10% each week, how much will be in the pond after 1 week passes? b. Write an equation to find the amount of herbicide in any given week. c. The landscaper will put another dose in the pond when the herbicide level reaches 50 gallons. In about how many weeks will he need to add more herbicide? 8 UNIT 3 Due: ____________ Name: ________________________________ 23) Beetles - A species of beetle's population grows 32% every year. Suppose 100 beetles are released into a field. a. Construct an exponential model for this population. b. How many beetles will there be in 10 years? c. How many beetles will there be in 20 years? d. About when will there be 100,000 beetles? 9 QUESTION 1 Minimum payment 4% 15.99% 1.33% Annual Percentage Rate Monthly Percentage Rate Month QUESTION 2 Invest Annual rate Term in years Amount after 10yrs QUESTION 3 Invest Annual rate monthly rate Term in years term inmonths Amount after 10yrs Starting balance 1 $ 2 $ 3 $ $ $ $ $ Finance charge 500.00 $ 6.66 486.66 $ 6.48 473.68 $ 6.31 100.00 5% 10 162.89 100.00 5% 0% 10 120 164.70 QUESTION 4 Lets assume staff is at double staff will be growth 200=100(1+5%)^n 2=1.05^n n=log 2.0/log 1.05 n(years) 100 200 5% 200/100=(100(1.05)^n)/100 log 2=n log 1.05 14.2066990829 14.21 QUESTION 5 Purchase price Down payment(20%) Amount to borrow $ $ $ 165,000.00 33,000.00 132,000.00 $ 132,000.00 30 360 4% 0.0033333333 209.4612404542 630.19 Mortgage Term in years Term in months APR APR(monthly) PVIFA Montly payment $ New balance $ 486.66 $ 473.68 $ 461.05 Interest over 30yrs QUESTION 6 Invest Annual rate monthly rate Term in years term inmonths PVIFA Amount after 20yrs $ 94,867.75 $ 150.00 3% 0% 20 240 180.3109144125 27,046.64 $ QUESTION 7 COUNTY Knox County Dubois County 2011 19.70% 8.30% 11.40% State/ County Name QUESTION 11 Charge Sales tax Charge is 107% of menu price Menu price is 100% menu price QUESTION 12 sells at marked down Charge is 140% of sale price sale price is 100% sale price QUESTION 13 dinner bill tip tip cash should be 2001 11.70% 9.00% 5.00% 9.00% 13.20% 10.50% 11.00% $ $ $ $ $ $ 131.21 7% 107% 100% 122.63 220.00 40% 140% 100% 157.14 32.00 15% 4.80 2011 Absolute change 15.90% 4.20% 15.80% 6.80% 8.30% 3.30% 18.30% 9.30% 19.70% 6.50% 21.40% 10.90% 21.10% 10.10% present gas pices price was up 6months ago by price was 6months ago $ $ 3.95 8% 4.27 Minimum payment $ 20.00 $ 19.47 $ 18.95 relative change 36% 76% 66% 103% 49% 104% 92% UNIT 3 Due: ____________ Name: ________________________________ Show all work. Make sure to show what values you used in any formulas. 1) You have to charge $500 of car repairs and no additional charges during the next two months, you will just pay the minimum payment each month for the next two months. The Annual Percentage Rate (APR) is 15.99% and the minimum payment each month is 4% of the balance. Determine the finance charge, new balance, and minimum payment required for each of the next two months, and the starting balance for month 3 in the table below: Month Starting balance 1 $500 2 3 Finance charge New balance Minimum payment 2) Find the balance on an account if you invest $100 at 5% for 10 years compounded annually. 3) Find the balance on an account if you invest $100 at 5% for 10 years compounded monthly. 4) A business finds that it has to increase its staff by 5% each year due to growth. After how many years would the size of their staff double? 5) Your friend purchases a $165,000 house. a. If he makes a 20% down payment, how much money will he borrow for his mortgage? 1 UNIT 3 Due: ____________ Name: ________________________________ b. The bank is willing to give him this mortgage on a 30 year loan with a 4% APR, what would you enter into Excel in order to find out his monthly payment? c. Excel would return a value of $630.19. How much interest will your friend pay over 30 years of his loan? 6) Your friend is able to invest $150 a month in a 401(k) with a predicted growth rate of 3% over 20 years. What would you type into Excel to find the predicted value in his 401(k)? 7) The Poverty Rate for Knox County in 2011 is ___________ percent more than the Poverty Rate of Dubois County in 2011. (See page 3 for the chart) Percent of All Ages in Poverty State / County Name 200 1 United States 11.7 Indiana 9 2011 15.9 15.8 2 UNIT 3 Due: ____________ Dubois County Elkhart County Knox County Tippecanoe County Wayne County 5 9 13.2 10.5 11 Name: ________________________________ 8.3 18.3 19.7 21.4 21.1 8) Find the Absolute Change in the Percent of those living in Poverty for the state of Indiana from 2001 to 2011. 9) Find the Relative Change in the Percent of those living in Poverty for the state of Indiana from 2001 to 2011. 10) Use the Relative Change you found in 9 to write a sentence explaining the change. 11) You are charged $13.21 total for a meal, assume the 7% sales tax, how much was the menu price of this item? 12) An item that normally sells for $220 is marked down by 40%. What is the sale price? 3 UNIT 3 Due: ____________ Name: ________________________________ 13) You plan to leave a 15% tip and your dinner bill is $32. How much tip money should you give? 14) If gas prices are now $3.95 and they were up 8% from 6 months ago, how much were gas prices 6 months ago? 15) According to the Ivy Tech website, students will pay a $60 technology fee and $121.50 per credit hour for Spring 2014. a. Set up a linear model to calculate a student's bill based on this information. Let X represent credit hour(s) and Y represent the total of technology fee and the credit hour(s) the student will take then the linear model will be: Y=121.50X+60 b. The independent variable in my model is X and it represents the value(s) that determine the value(s) of variable Y c. The dependent variable in my model is Y and it represents the values that are determined by the independent variable x d. Use your model to determine how many credit hours a student is taking if his bill is $1639.50? Y=121.5x+60; 1639.50=121.5x+60, 121.5x=1639.5-60; 121.5x=1579.5; x=1579.5/121.5=13 13hrs 16) You invest $230 to start a sandwich stand and decide to charge $4.25 per sandwich. a. Set up a Linear Model that determines your profit or loss based on the number of sandwiches. Let the number of sandwiches be X and profit be Y, the linear model will be Y=4.25X-230 b. How many sandwiches must you sell to break even? At breakeven there are zero profits therefore 0=4.25x-230; 4.25x=230; x=230/4.25= 54.12 sandwiches c. How many sandwiches must you sell to make a $100 profit? 4 UNIT 3 Due: ____________ Name: ________________________________ 100=4.25x-230; 4.25x=330; x=330/4.25= 77.65 sandwiches 17) The median adjusted income in Indiana in 1990 was $46,300 and in 2011 was $44,450. Find and interpret the average rate of change. Change=$(46300-44450) =$1850; average rate of change=changeumber of years when change took place = 1850/22= $84.09; medium adjusted income in Indiana has decreased with an average of $84.09 from 1990 to 2011 18) A can of soda in 1972 costs $0.10; by 2012 it cost $1.25. a. Construct a linear model that can be used to predict the cost of soda in a given year. Average rate of change= (1.25-0.1)/ (2012-1972+1)=1.15/41=0.02805 Let x be number of years, y represents the value of a can of soda at a given year The linear model thus will be y=0.02805x+0.10 b. Use your linear model to predict the cost of a soda in 2014. Years between 1972 and 2014 is 2014-1972+1=43=x Y=0.02805x+0.1; y=0.02805(43) + 0.1=$1.33 19) A scatter plot was made using data on tuition at Public 2 year colleges from 1964-2011 and a linear trend line was added. The equation and R 2 for the trendline are in the textbox on the graphic. Data from: http:/ces.ed.gov/fastfacts/display.asp?id=76 5 UNIT 3 Due: ____________ Name: ________________________________ Average 2 yr College Tuition 8,500 8,000 7,500 7,000 6,500 f(x) = 50.24x - 93935.1 R = 0.74 Dollars 6,000 5,500 5,000 4,500 4,000 1964 1974 1984 1994 2004 a. Use the linear model for the trend line to predict tuition costs for 2014. Y=50.245x-93935= 50.245*2014-93935=$7258.43 b. Find the r value for this regression line. What does it tell you? R=R2, r=0.7353= 0.8575 c. Should you use the linear model to predict tuition for 2025? Why or Why not? Yes. The value of R2 is between 0.7 and 1.0, indicating that there is a strong linear relationship thus you can use it to make predictions for 2025 tuition. 6 UNIT 3 Due: ____________ Name: ________________________________ Annual CPI 250.0 200.0 f(x) = 4.24x - 8315.16 R = 0.98 150.0 100.0 50.0 0.0 1960 1970 1980 1990 2000 2010 20) A scatterplot was made using the annual CPI rate from 1960 to 2014 and a trend line was added. a. What is the independent variable in this model, what does it represent? X is the independent variable whose values determine values of y b. What is the dependent variable in this model, what does it represent? c. Use the trend line equation to estimate the CPI for 2000. Y=4.244x-8315.2, Y=4.244(2000)-8315.2= 172.8 d. What can be said about the accuracy of this model? The value of R2 is between 0.7 and 1.0, thus it is within the recommended range of accuracy e. Interpret the meaning of the slope of the trend line. Slope of the trend line or rather the rate of change the trend line is 4.244 which means according to the trend-line, the CPI is increasing by 4.244 every year. f. Should we use this model to predict CPI for 2020? Why or Why not? Yes. The value of R2 is between 0.7 and 1.0, indicating that there is a strong linear relationship thus you can use it to make predictions for 2020. 7 UNIT 3 Due: ____________ Name: ________________________________ 21) To celebrate Ivy Tech's anniversary, a landscaper puts 50 water lilies on a pond the week before classes start. Unfortunately, every lily splits and produces a second lily once a week. a. Fill out this table for the number of lilies for the first few weeks: Week 0 Week 1 Week 2 Week 3 Week 4 50 100 200 400 800 b. Write an equation to find the number of lilies in a given week. Let x be number of weeks and y be the number of lilies in the pond; the y =2 x*50= 50(2x) Y=50(2x) c. How many lilies will be on the pond by week 16? Y=50(2x) =50*(216) =50*65536=3276800lilies 22) The landscaper pours 200 gallons of herbicide in the pond. a. If the herbicide degrades 10% each week, how much will be in the pond after 1 week passes? After 1 week=200(1-10%) =180gallons b. Write an equation to find the amount of herbicide in any given week. Y=200*(1-10%)x; y=200(0.9x), x is the number of weeks c. The landscaper will put another dose in the pond when the herbicide level reaches 50 gallons. In about how many weeks will he need to add more herbicide? Y=200(0.9x); 50=200(0.9x); (0.9x)=50/200; (0.9x)=0.25; x log 0.9= log 0.25; x= log 0.25/ log 0.9= 13.16 years 23) Beetles - A species of beetle's population grows 32% every year. Suppose 100 beetles are released into a field. a. Construct an exponential model for this population. Y=100ert where y is the expected number of beetles at time (t), r the growth rate and t time in years. b. How many beetles will there be in 10 years? Y=100ert; y=100e (32%*10); y=100e3.2 = 2453.25 beetles 8 UNIT 3 Due: ____________ Name: ________________________________ c. How many beetles will there be in 20 years? 24) Y=100ert; y=100e (32%*20); y=100e6.4 = 60184.50 beetles a. About when will there be 100,000 beetles? Y=100ert; y=100e (32%*t); y=100e0.32t = 100000 beetles; e0.32t=1000; this can also be put as 2.71830.32t=1000; 0.32tlog 2.7183= log 1000 thus 0.32t=log 1000/ log 2.7183; 0.32t=6.9078; t=6.9078/0.32= 21.59years 9 QUESTION 1 Minimum payment 4% 15.99% 1.33% Annual Percentage Rate Monthly Percentage Rate Month QUESTION 2 Invest Annual rate Term in years Amount after 10yrs QUESTION 3 Invest Annual rate monthly rate Term in years term inmonths Amount after 10yrs Starting balance 1 $ 2 $ 3 $ $ $ $ $ Finance charge 500.00 $ 6.66 486.66 $ 6.48 473.68 $ 6.31 100.00 5% 10 162.89 100.00 5% 0% 10 120 164.70 QUESTION 4 Lets assume staff is at double staff will be growth 200=100(1+5%)^n 2=1.05^n n=log 2.0/log 1.05 n(years) 100 200 5% 200/100=(100(1.05)^n)/100 log 2=n log 1.05 14.2066990829 14.21 QUESTION 5 Purchase price Down payment(20%) Amount to borrow $ $ $ 165,000.00 33,000.00 132,000.00 $ 132,000.00 30 360 4% 0.0033333333 209.4612404542 630.19 Mortgage Term in years Term in months APR APR(monthly) PVIFA Montly payment $ New balance $ 486.66 $ 473.68 $ 461.05 Interest over 30yrs QUESTION 6 Invest Annual rate monthly rate Term in years term inmonths PVIFA Amount after 20yrs $ 94,867.75 $ 150.00 3% 0% 20 240 180.3109144125 27,046.64 $ QUESTION 7 COUNTY Knox County Dubois County 2011 19.70% 8.30% 11.40% State/ County Name QUESTION 11 Charge Sales tax Charge is 107% of menu price Menu price is 100% menu price QUESTION 12 sells at marked down Charge is 140% of sale price sale price is 100% sale price QUESTION 13 dinner bill tip tip cash should be 2001 11.70% 9.00% 5.00% 9.00% 13.20% 10.50% 11.00% $ $ $ $ $ $ 131.21 7% 107% 100% 122.63 220.00 40% 140% 100% 157.14 32.00 15% 4.80 2011 Absolute change 15.90% 4.20% 15.80% 6.80% 8.30% 3.30% 18.30% 9.30% 19.70% 6.50% 21.40% 10.90% 21.10% 10.10% present gas pices price was up 6months ago by price was 6months ago $ $ 3.95 8% 4.27 Minimum payment $ 20.00 $ 19.47 $ 18.95 relative change 36% 76% 66% 103% 49% 104% 92% UNIT 3 Due: ____________ Name: ________________________________ Show all work. Make sure to show what values you used in any formulas. 1) You have to charge $500 of car repairs and no additional charges during the next two months, you will just pay the minimum payment each month for the next two months. The Annual Percentage Rate (APR) is 15.99% and the minimum payment each month is 4% of the balance. Determine the finance charge, new balance, and minimum payment required for each of the next two months, and the starting balance for month 3 in the table below: Month Starting balance 1 $500 2 3 Finance charge New balance Minimum payment 2) Find the balance on an account if you invest $100 at 5% for 10 years compounded annually. 3) Find the balance on an account if you invest $100 at 5% for 10 years compounded monthly. 4) A business finds that it has to increase its staff by 5% each year due to growth. After how many years would the size of their staff double? 5) Your friend purchases a $165,000 house. a. If he makes a 20% down payment, how much money will he borrow for his mortgage? 1 UNIT 3 Due: ____________ Name: ________________________________ b. The bank is willing to give him this mortgage on a 30 year loan with a 4% APR, what would you enter into Excel in order to find out his monthly payment? c. Excel would return a value of $630.19. How much interest will your friend pay over 30 years of his loan? 6) Your friend is able to invest $150 a month in a 401(k) with a predicted growth rate of 3% over 20 years. What would you type into Excel to find the predicted value in his 401(k)? 7) The Poverty Rate for Knox County in 2011 is ___________ percent more than the Poverty Rate of Dubois County in 2011. (See page 3 for the chart) Percent of All Ages in Poverty State / County Name 200 1 United States 11.7 Indiana 9 2011 15.9 15.8 2 UNIT 3 Due: ____________ Dubois County Elkhart County Knox County Tippecanoe County Wayne County 5 9 13.2 10.5 11 Name: ________________________________ 8.3 18.3 19.7 21.4 21.1 8) Find the Absolute Change in the Percent of those living in Poverty for the state of Indiana from 2001 to 2011. 9) Find the Relative Change in the Percent of those living in Poverty for the state of Indiana from 2001 to 2011. 10) Use the Relative Change you found in 9 to write a sentence explaining the change. 11) You are charged $13.21 total for a meal, assume the 7% sales tax, how much was the menu price of this item? 12) An item that normally sells for $220 is marked down by 40%. What is the sale price? 3 UNIT 3 Due: ____________ Name: ________________________________ 13) You plan to leave a 15% tip and your dinner bill is $32. How much tip money should you give? 14) If gas prices are now $3.95 and they were up 8% from 6 months ago, how much were gas prices 6 months ago? 15) According to the Ivy Tech website, students will pay a $60 technology fee and $121.50 per credit hour for Spring 2014. a. Set up a linear model to calculate a student's bill based on this information. Let X represent credit hour(s) and Y represent the total of technology fee and the credit hour(s) the student will take then the linear model will be: Y=121.50X+60 b. The independent variable in my model is X and it represents the value(s) that determine the value(s) of variable Y c. The dependent variable in my model is Y and it represents the values that are determined by the independent variable x d. Use your model to determine how many credit hours a student is taking if his bill is $1639.50? Y=121.5x+60; 1639.50=121.5x+60, 121.5x=1639.5-60; 121.5x=1579.5; x=1579.5/121.5=13 13hrs 16) You invest $230 to start a sandwich stand and decide to charge $4.25 per sandwich. a. Set up a Linear Model that determines your profit or loss based on the number of sandwiches. Let the number of sandwiches be X and profit be Y, the linear model will be Y=4.25X-230 b. How many sandwiches must you sell to break even? At breakeven there are zero profits therefore 0=4.25x-230; 4.25x=230; x=230/4.25= 54.12 sandwiches c. How many sandwiches must you sell to make a $100 profit? 4 UNIT 3 Due: ____________ Name: ________________________________ 100=4.25x-230; 4.25x=330; x=330/4.25= 77.65 sandwiches 17) The median adjusted income in Indiana in 1990 was $46,300 and in 2011 was $44,450. Find and interpret the average rate of change. Change=$(46300-44450) =$1850; average rate of change=changeumber of years when change took place = 1850/22= $84.09; medium adjusted income in Indiana has decreased with an average of $84.09 from 1990 to 2011 18) A can of soda in 1972 costs $0.10; by 2012 it cost $1.25. a. Construct a linear model that can be used to predict the cost of soda in a given year. Average rate of change= (1.25-0.1)/ (2012-1972+1)=1.15/41=0.02805 Let x be number of years, y represents the value of a can of soda at a given year The linear model thus will be y=0.02805x+0.10 b. Use your linear model to predict the cost of a soda in 2014. Years between 1972 and 2014 is 2014-1972+1=43=x Y=0.02805x+0.1; y=0.02805(43) + 0.1=$1.33 19) A scatter plot was made using data on tuition at Public 2 year colleges from 1964-2011 and a linear trend line was added. The equation and R 2 for the trendline are in the textbox on the graphic. Data from: http:/ces.ed.gov/fastfacts/display.asp?id=76 5 UNIT 3 Due: ____________ Name: ________________________________ Average 2 yr College Tuition 8,500 8,000 7,500 7,000 6,500 f(x) = 50.24x - 93935.1 R = 0.74 Dollars 6,000 5,500 5,000 4,500 4,000 1964 1974 1984 1994 2004 a. Use the linear model for the trend line to predict tuition costs for 2014. Y=50.245x-93935= 50.245*2014-93935=$7258.43 b. Find the r value for this regression line. What does it tell you? R=R2, r=0.7353= 0.8575 c. Should you use the linear model to predict tuition for 2025? Why or Why not? Yes. The value of R2 is between 0.7 and 1.0, indicating that there is a strong linear relationship thus you can use it to make predictions for 2025 tuition. 6 UNIT 3 Due: ____________ Name: ________________________________ Annual CPI 250.0 200.0 f(x) = 4.24x - 8315.16 R = 0.98 150.0 100.0 50.0 0.0 1960 1970 1980 1990 2000 2010 20) A scatterplot was made using the annual CPI rate from 1960 to 2014 and a trend line was added. a. What is the independent variable in this model, what does it represent? X is the independent variable whose values determine values of y b. What is the dependent variable in this model, what does it represent? c. Use the trend line equation to estimate the CPI for 2000. Y=4.244x-8315.2, Y=4.244(2000)-8315.2= 172.8 d. What can be said about the accuracy of this model? The value of R2 is between 0.7 and 1.0, thus it is within the recommended range of accuracy e. Interpret the meaning of the slope of the trend line. Slope of the trend line or rather the rate of change the trend line is 4.244 which means according to the trend-line, the CPI is increasing by 4.244 every year. f. Should we use this model to predict CPI for 2020? Why or Why not? Yes. The value of R2 is between 0.7 and 1.0, indicating that there is a strong linear relationship thus you can use it to make predictions for 2020. 7 UNIT 3 Due: ____________ Name: ________________________________ 21) To celebrate Ivy Tech's anniversary, a landscaper puts 50 water lilies on a pond the week before classes start. Unfortunately, every lily splits and produces a second lily once a week. a. Fill out this table for the number of lilies for the first few weeks: Week 0 Week 1 Week 2 Week 3 Week 4 50 100 200 400 800 b. Write an equation to find the number of lilies in a given week. Let x be number of weeks and y be the number of lilies in the pond; the y =2 x*50= 50(2x) Y=50(2x) c. How many lilies will be on the pond by week 16? Y=50(2x) =50*(216) =50*65536=3276800lilies 22) The landscaper pours 200 gallons of herbicide in the pond. a. If the herbicide degrades 10% each week, how much will be in the pond after 1 week passes? After 1 week=200(1-10%) =180gallons b. Write an equation to find the amount of herbicide in any given week. Y=200*(1-10%)x; y=200(0.9x), x is the number of weeks c. The landscaper will put another dose in the pond when the herbicide level reaches 50 gallons. In about how many weeks will he need to add more herbicide? Y=200(0.9x); 50=200(0.9x); (0.9x)=50/200; (0.9x)=0.25; x log 0.9= log 0.25; x= log 0.25/ log 0.9= 13.16 years 23) Beetles - A species of beetle's population grows 32% every year. Suppose 100 beetles are released into a field. a. Construct an exponential model for this population. Y=100ert where y is the expected number of beetles at time (t), r the growth rate and t time in years. b. How many beetles will there be in 10 years? Y=100ert; y=100e (32%*10); y=100e3.2 = 2453.25 beetles 8 UNIT 3 Due: ____________ Name: ________________________________ c. How many beetles will there be in 20 years? 24) Y=100ert; y=100e (32%*20); y=100e6.4 = 60184.50 beetles a. About when will there be 100,000 beetles? Y=100ert; y=100e (32%*t); y=100e0.32t = 100000 beetles; e0.32t=1000; this can also be put as 2.71830.32t=1000; 0.32tlog 2.7183= log 1000 thus 0.32t=log 1000/ log 2.7183; 0.32t=6.9078; t=6.9078/0.32= 21.59years 9