MATH 115 QUIZ 3 NAME: _______________________________ April, 2016 Instructor: S. Sands I have completed this assignment myself, working independently and not consulting anyone except the instructor. INSTRUCTIONS The quiz is worth 100 points. There are 11 problems. This quiz is open book and open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission). You may take as much time as you wish, provided you turn in your quiz no later than Sunday, April 17. Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. In your document, be sure to include your name and the assertion of independence of work. General quiz tips and instructions for submitting work are posted in the Quizzes module. If you have any questions, please contact me by e-mail. 1. (8 pts) (a) Let x=log 3 1 243 State the corresponding exponential form of this logarithmic equation. (b) Determine the numerical value of log 3 1 243 in simplest form. Work optional. 2. (8 pts) Use an appropriate change of base formula to approximate thousandth. Show some work. log6 30 to the nearest 3. (8 pts) Use the properties of logarithms to write the expression as a single logarithm and, if possible, simplify. Work optional. (1/2) log5 (x) - 2 log5 (y) - 3 log5 (z) 4. (8 pts) Expand x2 y log 3 10 z ( ) and simplify as much as possible. Assume all quantities represent positive real numbers. Work optional. 5. (8 pts) Solve: 4x= 1 128 Show work. 6. (12 pts) Solve: log (x2 + 2x - 3) - log(x - 1) = 2. Show work for solving and checking. 7. (5 pts) Students in a math class took a final exam (with a grade scale of 0 to 100) and then took equivalent forms of the exam at monthly intervals thereafter. The average grade g after t months was found to be given by the function g(t) = 77 6.5 ln(t + 1), t 0. (Note that "ln" refers to the natural log function) (no explanation required) (a) What was the average grade when the students initially took the exam, when t = 0? (b) What was the average grade on the exam when taken 3 months later? 8. (10 pts) (a) If $20,000 is invested in an account which offers 4.5%, compounded monthly, find the amount in the account after 18 years. Show some work. (b) If $20,000 is invested in an account which offers 4.5%, compounded continuously, find the amount in the account after 18 years. Show some work. 9. (13 pts) A cup of hot coffee was placed in a room maintained at a constant temperature of 72 degrees, and the coffee temperature was recorded periodically. t = Time C = Coffee Elapsed (minutes) Temperature (degrees F.) 0 10 20 30 40 50 60 169.0 143.5 128.2 113.3 107.5 101.4 96.9 Using exponential regression with the data set, the following temperature model was produced: C(t) = 72 + 89.976 e 0.023 t where t = Time Elapsed (minutes) and C(t) = Coffee Temperature (in degrees) at time t. (a) Use the temperature model to estimate the coffee temperature C when 5 minutes have elapsed. Report your estimated temperature to the nearest tenth of a degree. (explanation/work optional) (b) Suppose the coffee temperature C is 120 degrees. Solve an appropriate equation for t to determine how much time has elapsed. Show algebraic work to solve the equation. Report your answer to the nearest tenth of a minute. (c) Briefly describe what happens to the coffee temperature C(t) as the elapsed time t becomes larger and larger. Is this a realistic description of the behavior of the actual coffee temperature? 10. (12 pts) (no explanation required) (a) For the angle 280, what is the associated quadrant? (b) State a positive angle and a negative angle, in degrees, which are coterminal with the angle 280. (c) For the angle 5 6 , what is the associated quadrant? (d) State a positive angle and a negative angle, in radians, which are coterminal with the angle 11. (8 pts) Angle Conversion (a) Convert the angle 330 from degree measure into radian measure. Show some work. (b) Convert the angle 4 3 from radian measure into degree measure. Show some work. 5 6