Math Exam 03 Fall 2016

Transcription

1 Math Exam 03 Fall 2016 Name Class ID Number: Instructions: You will be required to show identification to take this exam. Bring your student ID to class. Please remove headphones during the exam. Hats or headcoverings without a brim may be worn. Hats with brims must be removed or turned backward. Show all work, as partial credit will be given where appropriate. If no work is shown, there may be no credit given. All final answers should be written in the space provided on the exam and in simplified form. When needed give your answer as an exact amount, i.e., a fraction or symbolic expression like e 2. Do not round decimals except for dollar amounts which should be rounded to the nearest cent. This is a closed notes/closed book exam - You are not allowed any outside aids during this exam. You will be provided with scratch paper. If you have any other papers at your desk during the exam you will be given a zero on the exam. The only calculators allowed during this exam are those on the approved calculator list. You are responsible for providing your own calculator. Cell phone, graphing and programmable calculators will not be allowed under any circumstances. Sharing of calculators is not allowed and will be considered a cheating offense. If your phone is out during the exam it will be considered a cheating offense - put your phone away! Be aware, I will not interrupt the exam to address a cheating. If you are caught cheating you grade for this exam will be a zero and you will be notified when your grade is posted on canvas.

2 Math Exam 03, Page 2 of December 2016 Question Points Score Evaluating Exponential and Logarithmic Expressions 10 Solving Logarithmic and Exponential Equations 14 Arithmetic and Geometric Sequences 10 Inverse Functions 12 Exponential Functions 4 Graph Transformation 1 10 Graph Transformation 2 10 Graph Transformation 3 10 Doubling Time 10 Sound Intensity 10 Bonus 5 Total: 105 This exam will be graded out of 100 points.

3 Math Exam 03, Page 3 of December 2016 I understand that by taking this exam early, I am agreeing not to discuss the exam with any of my classmates until Friday, 02 December I further understand that any evidence of cheating may result in a zero grade on this exam and failure of the course. Student Name: Student Signature: Date:

4 Math Exam 03, Page 4 of December 2016 PROBLEMS WILL BE GRADED FOR CORRECT ANSWER AND COR- RECT METHODS. BOX YOUR FINAL ANSWERS AND SHOW YOUR WORK Calculation Skills [10 points] 1. Evaluating Exponential and Logarithmic Expressions Calculate each of the following, Rounding to two decimal places where necessary. (a) log 2 (32) (b) log 25 ( 1 5 ) (c) Given log b (x) = 2, log b (y) = 3, log b (z) = 5, calculate log b ( x2 y ) log z b(xy). (d) Given log b (x) = 2 and log b (c) = 8, calculate log c (x).

5 Math Exam 03, Page 5 of December 2016 [14 points] 2. Solving Logarithmic and Exponential Equations Solve each of the following for x. (a) 3(4 3 x ) + 2 = 8 (b) log 7 (4 x) = log 7 (x 2 ) log 7 (2) (c) log 3 (x 2 ) log 3 (x + 3) = log 3 (x 5) (d) e x2 = e 4x e 12 (e) ln(x 2 ) = 4

6 Math Exam 03, Page 6 of December 2016 [10 points] 3. Arithmetic and Geometric Sequences (a) Given 2,6,18,54,162,..., calculate the 20th term of this sequence. Clearly write the formula you choose to use. (b) Given 50, 43, 36, 29,..., calculate the 50th term of this sequence. Clearly write the formula you choose to use.

7 Math Exam 03, Page 7 of December 2016 [12 points] 4. (a) Find the inverse function for f(x) = 3 x (b) In part (a) above, you found the equation for the inverse function. Describe in words and symbols how you would correctly verify that this equation is correct. (c) What is the inverse function of f(x) = ln(x)? (d) What is the inverse function of f(x) = 2 x

8 Math Exam 03, Page 8 of December 2016 Graphing [4 points] 5. Exponential Functions y = a x y = b x y = c x z = d x Based on the figure above, order the bases of the exponentials in ascending order and circle the correct statement below. A. 0 < d < c < b < a B. d < 0 < c < b < a C. 0 < a < b < c < d D. a < 0 < b < c < d E. 0 < b < c < d < a F. b < 0 < c < d < a G. 0 < a < d < c < b H. a < 0 < d < c < b

9 Math Exam 03, Page 9 of December 2016 [10 points] 6. Graph Transformation 1 Given f(x) = log 2 (x + 3) 6. (a) What is the corresponding reference function. (b) Graph the reference function and its asymptote. Label 3 points with their coordinates for full credit. (c) Graph f(x) and its asymptote. Label 3 points with their coordinates for full credit.

10 Math Exam 03, Page 10 of December 2016 [10 points] 7. Graph Transformation 2 Given f(x) = 2 x. (a) What is the corresponding reference function. (b) Graph the reference function and its asymptote. Label 3 points with their coordinates for full credit. (c) Graph f(x) and its asymptote. Label 3 points with their coordinates for full credit.

11 Math Exam 03, Page 11 of December 2016 [10 points] 8. Graph Transformation 3 Given f(x) = 2x 2. (a) What is the corresponding reference function. (b) Graph the reference function. Label 3 points with their coordinates for full credit. (c) Graph f(x). Label 3 points with their coordinates for full credit.

12 Math Exam 03, Page 12 of December 2016 Applications and Graph Interpretation [10 points] 9. Doubling Time The following population figure depicts mosquito population size as a function of time measured in years. Mosquito Population as a function of time Quantity of Mosquitos t (a) How long does it take for the population to double in size? (b) How many mosquitos are in the original population? (c) Assuming the population grows exponentially with base e, write the equation that describes population size as a function of time. (Your final equation should have only two variables: y and t.) (d) How many mosquitos are in the population after 4 years?

13 Math Exam 03, Page 13 of December 2016 [10 points] 10. Sound Intensity The loudness of sound is described by the equation L = 10log( I I 0 ) where L is the loudness of the sound, measured in decibels (db); I is the intensity of the sound, measured in w m 2 ; I 0 is the reference intensity measuring w m 2. w (a) How loud is a sound with intensity is 50I 0? m 2 If necessary, Round your answer to two decimal places. (b) How intense is a sound that is 80 db?

14 Math Exam 03, Page 14 of December 2016 [5 points] 11. Bonus (a) The following figure depicts the graph of a function. Sketch a graph of the inverse function on the figure (b) Calculate the inverse of f(x) = 3log(2 x)