Math 103 Exam 4 MLC Sample Exam. Name: Section: Date:

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1 Name: Section: Date: Signature: Do not start this test until your instructor says so. You will have exactly 50 minutes from this time to finish the test. Please show all work in the space provided. There are 10 questions on 6 pages. Without fully opening the exam, please check to make sure your exam is complete efore you egin. Please read instructions carefully. 1. You will need a pencil or pen, one calculator and this exam paper. Please clear everything else from your desk. (Please turn off or switch cell phones to manner mode and place in ackpack NOT on your person.). Calculators such as the TI89, TI-NSPIRE, Voyage 00, TI9, TI9+, HP49G, HP49G+, HP50G, Casio algefx.0, algefx.0pls or laptop, handheld, desktop and palmtop computers are NOT to e used. The use of cell phones, PDAs, Blackerries, head sets, or any other wireless device in the classroom is specifically prohiited. Please do not ask your instructor/proctors aout calculator use or mode. You must clear all programs from your calculator memory. Calculators cannot e shared.. Please look at overhead/oard for possile corrections to this exam. 4. Do not spend too much time on a particular prolem. Work the prolems that are simplest for you first. 5. There is no partial credit on the multiple choice or true/false questions. On the open-ended questions, the grading will e ased on your method. SHOW ALL OF YOUR WORK. NO WORK = NO CREDIT! DO NOT SKIP STEPS! You must show all work that supports your answer in order to get credit. Be neat and orderly. If you need additional space, use the ack of the exam pages. 6. Circle the letter of the correct answer for multiple choice or true/false questions. For open-ended questions, place your work and answers in the space provided. Answers can e in any form unless otherwise specified. For prolems asking for EXACT answers, leave in terms of fractions, π and numer. No credit will e given for decimal approximations when an EXACT answer is required. When solving equations, please put your answer in solution set form. For decimal answers, round to 4 decimal places unless otherwise specified. 7. Give measurement units (feet, degrees, etc.) when appropriate. 8. SIMPLIFY ALL ANSWERS as much as possile. 1

2 1. Suppose you have $7000 to invest. Which investment yields the greater return over four years:.7% compounded continuously or.8% compounded semiannually? Solve algeraically and please rememer to show all formulas and work in an organized manner to support your final answer/conclusion. (Round final amounts to nearest cents.).7% continuously.8% semiannually 1. You have $000 to invest. What interest rate is needed for the investment to grow to $5000 in 10 years if the interest is compounded continuously? Round your final interest rate to the nearest tenth of a percent. 10

3 . Consider the equation and graph of f ( x) = log 5 ( x + 5) and find the following. Work/steps MUST e shown for prolems laeled with asterisk (*). (a) the domain and range of f Domain: Range: () the equation of the asymptote(s) *(c) x-intercept(s) *(d) y-intercepts(s) *(e) Evaluate f(0). *(f) Find an equation for the inverse of f. (g) Find the domain and range of the inverse. Domain: Range: 16

4 4. Let log A, log 5 B, and log 7 C. Write = = = 5 log in terms of A, B, and C Write the expression as a single logarithm whose coefficient is 1. Use properties of logarithms to simplify and condense the expression as much as possile. log x + log( x 9) log log( x + ) 10 4

5 6. Solve each of the equations elow using EXACT VALUES. (Do not round.) Show all work and steps in detail. (a) log (4x 7) = x x () e + e 8 = 0 (c) e x 1 = 5 x (d) ln( x + 8) ln(x 5) = ln 4 6 5

6 Multiple Choice Circle the letter of the correct answer. ( points each) 7. Which of the following is an example of an exponential function? (a) f x 1 x ( ) = () x+ x f ( x) = (c) ( x) = ( ) + 5 f (d) f ( x) = 4x 7 (e) none are exponential functions 8. Which of the following is the est estimate (nearest thousandths) of log 5 8? (a).65 ().774 (c) 1.9 (d) (e) none of these x x 1 9. If =, then x is equal to (a) () (c) 4 (d) (e) none of these Determine whether each statement is always true (T) or not always true (F). (Assume a,, x, and y are positive numers and are not equal to 1.) (a) log 8 = 1+ log 8 T F () ln ln a a = T F (c) (d) 1 log = T F log log10 x x = T F (e) log x log y = log x log y T F 10 Prolem # Total Points Earned Possile