M1030 Math 1030 Departmental Final Examination Fall 2007Name: _______________________________Instructor's Name:_______________________ Section: _________Instructions: Please note that there are two parts. Part I is worth a total of 30points. Part II is worth 70 points. Show your work on each question.The formulas below are provided for your convenienceSavings Plan: A = PMT € 1+APRn      ( nY )−1        APRn      Loan: PMT = € P ×APRn      1− 1+APRn      (−nY )        Final Examination Score : ____________Part I: (30 pts) There are five questions and each question is worth 6 points.1. Time magazine (November 16th, 2007):” 1,500– Number of tigers in India's reservesand jungles, which reflects a 40% drop in the past five years. The Indian government saysit plans to recruit soldiers to patrol tiger sanctuaries.”How many tigers dud India’s reserves and jungles have 5 years ago. Answer _________2. If you deposit $2,100 now and you can get an APR of 2.25% compoundedcontinuously, how much will you have in 30 years?Answer__________3. You plan to travel to Nepal and you are practicing how to deal with differentmeasurement systems. Consider the following situation.Suppose, an outdoor market in Nepal offers apples priced at 28 Nepalese Rupees perkilogram. What is the price of these apples in US dollars per pound if 1 US dollar is71.08 Nepalese Rupees and 1 kilogram is 2.2 pounds.Answer ___________4. The shape below with the given dimensions is a scale model of a cylinder. Thecylinder will be scaled down so that the new cylinder will have a height of 4 inches. Whatwill the surface area and the volume of the model be?Model height = 15 insurface area = 1060.3 in2volume = 2650.7 in3Surface area of the new cylinder______Volume of the new cylinder _______5. Your house was appraised at $ 369,000 in 2003. If you assume that the housing marketis steadily going up at a rate of 5.5%, how much will you house be worth in 2015?Answer ______________Does this situation represent a linear or exponential model? Why?Part II (70 pts): There are 7 questions and each question is worth 10 points.1. A certain medication breaks down in the human body (decreases) at a rate of 12% perhour.a) Find the approximate half-life. Answer ____________b) How long will it take for this drug (in your bloodstream) to reduce to 15% of theoriginal amount? Answer ____________c) If the initial dose was 500 mg, how much (in mg) is left in your bloodstream after 2days? Answer ___________2. You plan to buy one of two extra gas tanks shown below to take in your Jeep for off-roads trips. Tank A is a rectangular box with a base of 18 cm by 25 cm and height equalto 30 cm. Tank B is a cylinder with radius 6 inches and height 7.5 inches.a) Determine the volume of each tank using appropriate units. A B Volume of A ______Volume of B _______b) Which tank will have the greater volume? Recall: 1 inch = 2.54 cmAnswer ___________3. The following data represents measurement of the concentration of a substance in apatient’s bloodstream, after the start of a treatment meant to boost the concentration:Days after start of treatment 3 5 8 15Concentration in ppm 2.6 3.2 4.1 6.2a) Create a linear equation that would represent this situation. Answer _____________b) How long will it take for the concentration to reach 35 ppm?Answer ___________4. A savings account pays an annual percentage rate of 2.5% compounded quarterly.a) Find the annual percentage yield on this account. Answer ___________b) You decide that you would like to make regular quarterly deposits to this account.Since you would like to have $700,000 when you retire 40 years from now, how muchshould your quarterly deposits be in order to accomplish your goal? Answer ___________5. The doubling time of a state’s population is 24 years.a) If the population was 2,200,000 in 1995, what will the population be in 2028?Answer ___________b) If the population was 2,200,000 in 1995, how long will it take for this state to reach apopulation of 3,700,000? Answer ___________6. There are 80 cars on a used car lot. Out of those 80 cars, 24 are Ford and 31 areDodge, and 25 are red cars. There are 8 red Ford, and 10 red Dodge cars.a) Draw a Venn diagram to illustrate this information. Use the symbols F, D, R torepresent the set of Ford, Dodge, and red cars respectively.b) Use your diagram to answer the following:How many cars (on this lot) are red, but are not Ford and not Dodge. Answer _______How many cars (on this lot) are not red, not Ford, and not Dodge. Answer _______7. You have found that you are eligible for a 20-year house loan with annual interest rate(APR) of 6.25%, compounded monthly.a) What will your payment be if the loan amount is $280,000? Answer ____________b) What will be the total amount of interest (in dollars) that you will pay on this loan over20 years?Answer ___________c) You decide instead to get the same loan, but with a 15-year term. What are yourmonthly payments, and how much interest will you save (in dollars), compared to the 20-year loan. Monthly payment ___________ Interest saved