Take-Home Quiz # 3 (Sections 6.2-6.5, 10.1) Math 115/6383, Due 11:59PM, Sunday February 16, 2020 Instructions: This quiz must be completed independently. You are allowed to consult with your notes or the textbook as needed to aid you in solving these problems. Seeking help from others in or out of the class is not allowed. Suggestions about how to approach this quiz: 1. Finish all homework assignments of the sections and get good understanding of the contents from the last week. 2. Print out a copy of the quiz and solve any problems that you can, using pencil and paper. 3. Review the eBook sections associated with any problems you could not solve. 4. Complete the remaining problems to the best of your ability. Even if you cannot come to a final solution, you should show what you do know so that you have the opportunity for partial credit. 5. Review your work. Check for errors. Make sure you have included units where appropriate, and explanations when required by the instructions. Unless the problem explicitly states otherwise, work must be shown for every answer. Any answer, even if “correct” but lacking work, will NOT receive full credit and may receive NO credit! 6. When you are satisfied, type in your solutions (extend space if needed) or, if you have the facilities, you can scan your hand written work or take photos with your camera. Make sure that your submission is readable and is a single document. 7. Submit your work in the associated LEO assignment. Unless the problem explicitly states otherwise, work must be shown for every answer. Any answer, even if “correct” but lacking work, will NOT receive full credit and may receive NO credit! Please submit the quiz as an attachment in any readable formats such as scanned or photocopy before or on Sunday, February 16. No late quiz will be accepted. No make-up quiz will be arranged. A solution key for Quiz # 3 will be posted after 12pm (EST), Monday, February 17. Please sign (or type) your name below the following honor pledge: I have completed this quiz by myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz. Name ________________ _____ Date_____________________ QUIZ # 3 Problems 1. (8 pts) 1 to exponential form 3125 (a) Convert x = log 5 (b) Evaluate log 5 2. (8 pts) Evaluate log4100 to the nearest hundredth. Show some work. 1 . Do not use a calculator. Show some work. 3125  x 5 y1/ 4   and simplify as much as possible. Assume all quantities (8 pts) Expand log  3   8w  represent positive real numbers. Show some work. 3. 4. (8 pts) Use the properties of logarithms to write the expression as a single logarithm and, if possible, simplify. Show some work. (1/4) log3 (6x) – log3 (y) – 4 log3 (w) 1 . Do not use a calculator. Show work. 81 5. (8 pts) Solve: 27 x = 6. (12 pts) Solve: log 12 (36 − 36 x 2 ) − log 12 (1 + x) = 2 . Show work for solving and checking. 7. (5 pts) The home-ownership rate is the percentage of households that are owner-occupied. Based on data of U.S. home-ownership rates in the second half of the twentieth century, the following logarithmic model was determined: h(t) = 375.2 ln(t) - 2815.4, where t = year and h(t) = home-ownership rate, in percent. (Note that "ln" refers to the natural log function) (no explanation required) Using the above model, what was the home-ownership rate in 1990, to the nearest tenth of a percent? Show some work. 8. (10 pts) (a) If $6,000 is invested in an account which offers 4%, compounded monthly, find the amount in the account after 15 years. Show some work. (b) If $6,000 is invested in an account which offers 4%, compounded continuously, find the amount in the account after 15 years. Show some work. 9. (13 pts) A cup of hot coffee was placed in a room maintained at a constant temperature of 69 degrees, and the coffee temperature was recorded periodically. t = Time C = Coffee Elapsed (minutes) Temperature (degrees F.) 0 10 20 30 40 50 60 166.0 140.5 125.2 110.3 104.5 98.4 93.9 Using exponential regression with the data set, the following temperature model was produced: C(t) = 69 + 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 13 minutes have elapsed. Report your estimated temperature to the nearest tenth of a degree. Show some work. (b) Suppose the coffee temperature C is 100 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 262°, what is the associated quadrant? (b) State a positive angle and a negative angle which are coterminal with the angle 262°. (c) For the angle (d) State a positive angle and a negative angle which are coterminal with the angle 5 , what is the associated quadrant? 8 5 . 8 11. (8 pts) Angle Conversion (a) Convert the angle 240° from degree measure into radian measure. Show some work. (b) Convert the angle 7 from radian measure into degree measure. Show some work. 6 11.3.1 Exercises In Exercises 1 - 10, use the Law of Cosines to find the remaining side(s) and angle(s) if possible. 1. a = 7, b = 12, γ = 59.3◦ In Exercises 21 - 30, use the results developed throughout the section to find the requested value. 24. If cos (θ)=−2 11 with θ in Quadrant III, what is the sin(θ)?
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