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 |
Finance charge |
New balance |
Minimum payment |
| 1 |
$500 |
|
|
|
| 2 |
|
|
|
|
| 3 |
|
|
|
|
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.lf he makes a 20% down payment, how much money will he borrow for his mortgage?
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
|
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 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?
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
16) 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.
17) 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.
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?
18) 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?
19) 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 |
50 |
| Week 1 |
|
| Week 2 |
|
| Week 3 |
|
| Week 4 |
|
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?
20) 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?
21) 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?