MAT 142 – Topics In Math Exam 2 Spring 2012 CRN 20255 and 22750 Instructor: Robert Foth Pima Community College, Community Campus Answer the questions in the spaces provided. If you need additional space use the back of the page and make sure the problem number is referenced with the work. If scratch paper is used make sure to attach the paper along with the exam when it is turned in. You must show all work to receive full credit on the problem. You may use a calculator (may not use a cell phone). I will allow one 3x5 or 4x6 (inches) note card for the exams but you must turn it in with your exam. There is a two and a half hour time limit. Be sure to read each question carefully and follow the instructions given. It is possible to score over 100% on the exam. Good luck! I will grade each question based on: 1. Completeness - Showing all of your work and how you derived the answer. 2. Correctness - Getting the correct answer is important, but I will give partial credit if you show your work. 3. Neatness - I need to be able to read your answer. If I cannot read your answer/work, then you will receive 0 points for the problem. Students Name:________________________________________________________ SCORE ___________________ / 100 1. Determine how many smileyy faces will be in the tenth plus created (N=10). Construct an algebraic formula to determiine how many smileys will be in the 200 th Plus created and use that formula to find the answ wer (make sure to use N as the input variable forr your model). (8 points) 2. (4 points) Did you use inductive or dedductive reasoning to find the answer in #1. Explaain. 3. A system of linear inequalities is shown below. Graph the solution set. 2 x  y  1   x y 5 (8 points) 4. (8 points) ACME department stores is having a sale today. In the store ACME is advertising an everything is 20% off their already low price sale. In addition you can take an extra 30% off your entire purchase with your super store discount coupon you just found in the Newspaper today (says it can be combined with other offers). What is the total percent off at the cash register (ignore sales tax) if you were to first apply the 20% discount and then a 30% off discount when checking out? Hint: Consider your purchases was a total of $100 before applying the discounts. 5. Below is a scenario for a Linear Programming problem. You are about to take a test that contains computation problems worth 6 points each and word problems worth 10 points each. You can do a computation problem in 2 minutes and a word problem in 4 minutes. You have 40 minutes to take the test and may answer no more than 12 problems. Assuming you answer all the problems attempted correctly, how many of each type of problem must you answer to maximize your score? What is the maximum score? (i) Describe what the objective function is for this scenario and write out the objective function (make sure to define the variables used in your objective function). (6 points) (ii) Describe what a “constraint” is for a linear programming problem and list out the constraints for the scenario described above. (6 points) 6. (8 points) You invested into ACME on the New York Stock Exchange. On the first day the stock price rose by 10% and the second day the price dropped by 10%. Did you break even, make a profit, or realize a loss after the second day? Explain your reasoning below. 7. What type of model is a better fit for the data shown (linear or exponential)? Explain/Justify. You do not need to find the model itself – just explain which type you choose and why. X 2003 2004 2005 2006 2007 2008 Y 38 75 150 301 598 1215 (6 points) 8. Bank A offers a CD that pays a simple interest rate of 5.3%. Bank B offers a CD that pays an interest rate of 5.1% compounded monthly. In each circumstance explain which bank CD you would choose to use for your $500 investment. (i) You know you are going to need some case one year from now for next years tuition. Which bank CD would you choose and how much cash would you have? (6 points) (ii) (6 points) You plan on buying a new car four years from now. Which bank CD would you choose and how much cash would you have for that down payment? 9. A depositor opens a new savings account with $6000 at 5% compounded semiannually. At the beginning of year 3, an additional $4000 is deposited. At the end of six years what is the balance in the account? (6 points) 10. A depositor invests $25 at the end of each month in an IRA that has an annual rate of 5.2% compounded monthly. (6 points each) (i) How much will be saved at the end of 30 years? (ii) How much of this total was interest? 11. You plan on making two fixed deposits a year for the next 30 years to have for retirement. Your goal is to have $500,000 at the time of retirement in this account. You plan on investing in an annuity that pays 6.5% compounded semiannually (twice a year), what must those payments be every six months? (6 points) 12. The price of a house you’re looking at is $140,000. The bank requires you to make a 10% downpayment on the house and is willing to give you a 30-year fixed mortgage at 5.2%. Answer the following. (i) What is the required down payment? (3 points) (ii) What is the amount of the mortgage? (3 points) (iii) What are the monthly payments (ignore escrow and insurance) – round to nearest dollar? (6 points) (iv) (4 points) What is the total cost for the house if the payments are all made after 30 years?