MATH 1030, Review B for Exam 2
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1 MATH 1030, Review B for Exam 2 Name: 1. After 13 years of quarterly payments of $ 83, I finally paid off my (fixed rate) mortgage. (a) If the mortgage had an APR of 9%, what was my starting loan principal? (b) How much money did I spend paying off my mortgage? (c) How much money did I spend just on the interest? 2. Charles invests $1700 in an account with annual compounding and an APR of 6.6%. Denzel invests $1500 in an account with continuous compounding and an APR of 6.3%. (a) How much does Charles have after 5 years?
2 (b) How much does Charles have after 25 years? (c) How much does Denzel have after 5 years? (d) How much does Denzel have after 25 years? 3. The day before I am cryogenetically frozen for a millennium, I deposit 65 cents in my bank account. If my account has an APR of 3.45% compounded daily, how much money will I have when I wake up? 4. Judy deposits $50 per month in an account with an APR of 7%, while Mickie deposits $700 at the end of each year in an account with an APR of 7.5%. (a) How much does Judy have after 10 years?
3 (b) How much does Mickie have after 10 years? (c) How much does each person deposit over the ten years? 5. Assume your account compounds continuously at an APR of 2.3% (a) If you need $75, 000 a year for expenses, how much money will you need to live off interest alone? (b) Based on your answer to part(a), how much money should you deposit now if you want to retire in 45 years? 6. You want to buy an $18, 000 car. Let s consider two options: (a) You decide to save up and buy the car in 4 years. Your bank account has an annual percentage rate of 4.7%.
4 i. How much should you deposit each month? ii. What percentage of the $18, 000 will come from actual deposits? iii. What percentage of the $18, 000 will come from interest? (b) You decide to buy the car now on an installment loan. Your loan has an APR of 12%. i. How much money will you need to deposit each month to pay off the loan in 4 years? ii. What will be the total cost of the loan?
5 iii. What percentage of the total cost will be interest? 7. Suppose that my bank account compounds monthly at an APR of 5.6%. If I haven t touched the account since I made my initial deposit 11 years ago, how much money was in my account 5 years ago if my current balance is $2000? 8. On February 14 through February 19, 2003, a record-breaking snowstorm called the Presidents Day Storm of 2003 caused over 14 million dollars in damage for North American cities along the east coast. Garrett County, Maryland, received 36 inches of snow during the storm. Assume the snow fell at a constant rate. (a) What is the independent variable? (b) What is the dependent variable? (c) Write down a linear function describing the relationship between the independent and dependent variables. (d) What units are used for the dependent variable? (e) What units are used for the independent variable? (f) Give an appropriate domain for the function you wrote.
6 (g) What is the range? (h) How much snow had Garrett Country received after 36 hours of the blizzard? (i) Plot the function. 9. In July 2000 you measured the circumference of a tree in the park. It was 36 inches. In July 2004, you measured that the circumference of the same tree had grown to 44 inches. Assume that the circumference grew at a constant rate. (a) What is the independent variable? (b) What is the dependent variable? (c) Write down a linear function describing the relationship between the independent and dependent variables. (d) What units are used for the dependent variable? (e) What units are used for the independent variable? (f) Give an appropriate domain for the function you wrote.
7 (g) What is the range? (h) How old was the tree in 1999? (i) Plot the function. 10. A little boy and his older brother have a race. On his tricycle, the little boy can attain a speed of a mile an hour, while his brother can travel 2.4 miles in 15 minutes. To be fair, the little boy gets a 1 mile head start. Assume that they maintain constant speeds. (a) Write down a linear function for the little boy. (b) Write down a linear function for the older brother. (c) Plot both functions on the same axis.
8 (d) What will the distance between them be after 10 minutes? 11. Solve for x in each of the following equations: (a) 16 x = 4 (b) 3 7 x = 435 (c) 2 x/4 = A prominent restaurant in Paris is reported to have a rat infestation. Unfortunately, having not seen many animated Disney movies, the restaurant s patrons do not know that the rats are actually the brains behind the restaurant s culinary successes. When word spreads about the rats, the number of patrons decreases by 86% each month (30 days). (a) Find the half life for the number of patrons. (b) By what percentage has the number of patrons decreased in a day?
9 (c) By what percentage has the number of patrons decreased in a week? 13. Based on my current means, I can deposit $ 125 each month into my savings account. If my account has an APR of 5.4%, how long will it take me to reach my goal of becoming a millionaire? 14. A brilliant but twisted programmer writes a computer virus that spreads pretty quickly. When you get infected, it sends an to all of your friends (from your computer) with the subject i luv u. Your friends, desperate for your love, open the and get infected. So in some sense, this virus is not so much exploiting a vulnerability in computers as much as it is exploiting a vulnerability in the human condition. The number of infected computers increases by 45% per day. Initially, only 1 computer is infected. (a) Find the equation of an exponential model of the given situation. (b) How many computers will be infected in 7 days?
10 (c) What is the doubling time for the virus? 15. Hickory Jack has an ostrich farm. He started this farm 15 years ago with 4 ostriches, and now he has 167. (a) Find the equation of an exponential model of the given situation. (b) How many will he have in another 15 years? (c) What is the doubling time for the ostriches? 16. A civil war in the country of Exponia is causing hyperinflation. In fact, prices are doubling every two months. (30 days in a month) (a) Find the equation of an exponential model of the given situation.
11 (b) How much will a loaf of bread costing 4 Exponian dollars now cost in a week? (c) How about in a year?
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Math 1090 Final Exam Fall 2012 Name Instructor: Student ID Number: Instructions: Show all work, as partial credit will be given where appropriate. If no work is shown, there may be no credit given. All
r 1. Discuss the meaning of compounding using the formula A= A0 1+
Money and the Exponential Function Goals: x 1. Write and graph exponential functions of the form f ( x) = a b (3.15) 2. Use exponential equations to solve problems. Solve by graphing, substitution. (3.17)
Logarithmic and Exponential Functions
Asymptotes and Intercepts Logarithmic and exponential functions have asymptotes and intercepts. Consider the functions f(x) = log ax and f(x) = lnx. Both have an x-intercept at (1, 0) and a vertical asymptote
3. Joyce needs to gather data that can be modeled with a linear function. Which situation would give Joyce the data she needs?
Unit 6 Assessment: Linear Models and Tables Assessment 8 th Grade Math 1. Which equation describes the line through points A and B? A. x 3y = -5 B. x + 3y = -5 C. x + 3y = 7 D. 3x + y = 5 2. The table