Practice Exam #2 Math 1160

Transcription

1 Practice Eam # Math 60 The material on this eam does not cover all of the possile topics that could e on the real eam. This practice eam is meant as supplement to the normal studying routines efore eams. It is imperative that you look over all course materials and do not rely on the practice eam to give you the prolems. Other materials you should study: Quizzes Homework Notes from lecture and discussion Practice Eam Supply and Demand prolems! To e successful on a math test you must start studying early. Waiting until the night efore is usually a recipe for disaster! Leave yourself time to ask questions, stay rested, and rela! P age

2 .) You are in charge of purchases at the student run ookstore at your college and you must decided how many calculus, history, and marketing ooks you must purchase from students for resale. Due to udget restrictions, you cannot purchase more than 650 ooks each semester. There are also shelf limitations: Calculus ooks take up inches of space, History ooks take up inch of space, and Market ooks take up 3 inches of space. The student run ook store only has 000 inches of shelf space availale. If the used ook program makes a $0 profit of each Calculus ook, $4 per History ook, and $8 on each Marketing ook, how many of each type should you purchase? SET UP THE PROBLEM. DO NOT SOLVE. Decision Variales (with description): Ojective Function: Suject to constraints: P age

3 .) Use the following graph and matching system of linear inequalities to answer the following questions. Ojective function Suject to P = 0 + +, a). On the graph area provided, indicate the solution region ). Determine all the corner points associated with the region. c). Maimize and minimize P = suject to the constraints provided. 3 Page

4 3.) Solve the following maimization prolem using the graphical method. P = 0+ y + y 4 + y y, 0 4.) Solve the following system of equations using the graphical method and state whether the feasile region is ounded or unounded: Minimize C = 3 + Suject to: 0 8, P age

5 5.) Solve for : 3 log + log 5 log 0 = log 6.) Solve for : Solve for : = 0 7.) Use the following f ( ) = to answer the following:.) Indicate the verte c.) Find the maimum or minimum, eplain d.) Find the ais of symmetry e.) Find the and y intercepts f.) Graph the function laeling all of the aove (intercepts, y,, ais of symmetry, verte, ma or min) 5 P age

6 8.) Solve the following equations for a.) 0 = 0.) 3 ( + ) = 0 3 c.) = ) Suppose that $,500 is invested at 8% compounded quarterly. How much money will e in the account after a.) 6 months?.) years? c.) 0 years? 0.) Solve the following logarithmic function 3 log 4 log 8 + log = log 3.) Rewrite the following function in logarithmic notation y = 0 6 P age

7 .) $3,000 is invested for years at 3% per year. Compute the simple interest for the specified period and the future value at the end of the period. (Round all answers to the nearest cent.) 3.) An investment earns 6% per year and is worth $60,000 after years. Find the present value of the investment using simple interest. (Round your answer to the nearest cent.) 4.) Calculate, to the nearest cent, the future value of an investment of $0,000 at 3.5%/year compounded quarterly (4 times/year) after 5 years. 5.) Find the effective annual interest rate of % compounded monthly. Round your answer to the nearest 0.0%. 6.) You deposit monthly $000 in an account at the Lifelong Trust Savings and Loan that pays 4% interest compounded quarterly. By how much will your deposit have grown after 6 years? 7 P age

8 7.) The market research department of the Better Bay Buggy Co. predicts that the demand equation for its uggies is given y q =.5p + 800, where q is the numer of uggies it can sell in a month if the price is $p per uggy. At what price should it sell the uggies to get the largest revenue? What is the largest monthly revenue? 8.) How much do you need to save per week in order to reach a retirement goal of 3 million dollars in 35 years if you are certain you can get 8% interest? 9.) How long will a saving of million dollars last you if you withdraw $5,000 per month and your savings account accrues 4% interest? 8 P age