Math 140: Unit 8

Target Date: Tuesday Nov. 17
Deadline: Friday Nov. 20

Note: The information on this page is for the 8th edition of the textbook.
Click here for the 7th edition information.
Click here for the 6th edition information.

Table of Contents:

Topics
Study Guidelines
Unit Pretest and Exam Description
Checklist

Topics

Unit 8 continues the study of exponential and logarithmic functions, with a heavy emphasis on applications. The unit begins with a study of the important and very useful logarithm properties, followed by techniques for solving logarithmic and exponential equations. The skills that you learn in these two sections will then be used to solve real-world problems involving compound interest, population growth, radioactive decay, and temperature change.

• Properties of Logarithms (5.5)
  • Bases other than 10 or e
• Solving logarithmic and exponential equations (5.6)
  • Exact solutions using properties of logarithms and exponentials
  • Approximate solutions using a graphing calculator
• Applications
  • Compound interest (5.7)
    • Discrete compounding (n times per year)
    • Continuous compounding
    • Present value
  • Exponential growth and decay (5.8)
    • Uninhibited population growth
    • Radioactive decay
    • Newton's Law of Cooling
    • Logistic growth models
  • Logarithmic scales (5.4)
    • pH scale
    • Loudness of sound
    • Earthquake magnitude (Richter scale)

Study Guidelines for the 8th edition of Sullivan's Precalculus

These reading and problem assignments are designed to help you learn the course material. You should complete all of these problems, check your answers in the back of the textbook, and get help with the problems that you missed. Most of the problems are odd-numbered, so you can check the solutions in the Solutions Manual.

The only way to learn mathematics is to do mathematics, so while these problems will not be collected or graded, you will probably not do well in the course if you do not complete these and check your work as described above. After completing these problems, go on to the Unit Exam Description below and follow directions.

• Section 5.5: Properties of Logarithms
  • Review sections 5.2-4 before you begin this section.
  • Reading: section 5.5
    Read and work through examples 1-8 and their matched problems.
  • Practice Problems: 5.5 #9, 11, 13, 17, 19, 21, 23, 25, 29, 33, 37, 39, 41, 43, 49, 51, 53, 57, 59, 65, 67, 69, 71, 75, 77, 79, 81, 83, 85, 87
    
    
• Section 5.6: Logarithmic and Exponential Equations
  • Reading: section 5.6
    Read and work through examples 1-7 and their matched problems.
  • Some equations cannot be solved exactly. In this case, it is important to be able to find approximate solutions using the graphing capabilities of your calculator. The procedure outlined in example 7 uses the "INTERSECT" calculator routine. See appendix B.4 for brief calculator instructions, and see your calculator manual or Graphing Calculator Help for more detailed instructions.
  • Practice Problems: 5.6 #1-4, 9, 13, 17, 25, 31, 37, 39, 45, 49, 61, 69, 73, 79, 85, 99
    
    
• Section 5.7: Compound Interest
  • Review "Simple Interest" on pages A63-A64 of appendix A.8 before you begin this section.
  • Reading: section 5.7
    Read and work through examples 1-7 and their matched problems.
  • Additional examples of compound interest applications
  • Practice Problems: 5.7 #1, 2, 3, 7, 11, 13, 17, 21, 29, 31, 35, 39, 45, 48, 49, 53, 55, 63, 65
    
    
• Section 5.8: Growth and Decay; Newton's Law; Logistic Models
  • Reading: section 5.8
    Read and work through examples 1-6 and their matched problems.
  • Additional examples of exponential growth and decay applications
  • Try out two java applets that let you explore logistic models and Newton's Law of Cooling.
  • Practice Problems: 5.8 #1-15 odds, 21, 25
    
    
• Section 5.4: Logarithmic Scales
  • Several examples of logarithmic scales are given in the exercises of section 5.4:
    • pH scale for measuring the acidity or alkalinity of a chemical solution
    • decibel scale for measuring loudness of sound
    • Richter scale for measuring the magnitude of an earthquake
  • Practice Problems: 5.4 #117, 127-130, 131, 132
  • Additional discussion, examples, and exercises involving logarithmic scales.
    This supplement includes a discussion on an equivalent version of the Richter scale formula which measures the "size" of an earthquake in terms of the actual energy released by the earthquake.
    
    
• Supplementary material (optional):
  • Student Solutions Manual
  • Algebra Review booklet
  • CD lecture series (step-by-step video examples on CD)
  • For tutoring help, visit the Prentice Hall Tutor Center. Tutors can be contacted by phone, fax, or e-mail. To register, you will need the access code that came with your textbook.
  • Graphing Calculator Help

Unit 8 Pretest and Exam Description

After completing the above work, do the following:

1. Read the exam description:
   • This exam has 15 questions, and will count 15 points toward your grade. 9 of the 15 problems are applications problems.
   • The exam has a one hour time limit.
   • You will need your graphing calculator on this exam. In particular, you will need to know how to use your graphing calculator to graph logarithmic and exponential functions and to find approximate intersections of curves (as in example 7 and exercises 61-74 of section 5.6).
   • Some problems ask for exact answers, but others ask for an approximation to a certain accuracy. For example, if you are asked to give an answer that is "accurate to at least two decimal places", and your answer is 4.6792, then you would have to enter at least two digits after the decimal point, i.e., you could enter 4.67, 4.679, 4.679, or even 4.68. When you view your corrected exam, you will see that the "correct" answer is given in the form 4.6792  0.01. The symbol means "plus or minus", so anything within 0.01 of the first number counts as correct.     
          On the other hand, if instead you are asked to "round your answer to the nearest integer", then you would enter 5 if your actual answer is 4.6792, and you would enter 4 if your actual answer is 4.3792.
   • Be sure to look under the entry box for the expected format of the answer.
     • Some problems ask you to solve a problem which may have more than one solution. If there is more than one solution, separate the solutions with a semicolon. For example, your answer might be 3;5. In this case, the order of the values is not important.
2. Complete the online Unit 8 Pretest assignment. You may use your book and notes if you wish.
   • Directions: Click on the link above, then choose the Unit 8 Pretest.
   • The pretest must be completed by the deadline date listed at the top of this page.
     However, you may redo the pretest as many times as you like before the due date.
     Your best score counts, and it will be rescaled to 5 points maximum.
3. If you are having trouble with any of the problems listed above or on the pretest, make use of the help resources listed on the Help page.
4. Arrange with your proctor to take the online proctored Unit 8 Exam. Remember to bring identification, and remember that you will not be able to take the unit exam after the deadline date given at the top of this page. You may NOT use your book or notes on this exam.
   • Directions: Click on the link above, then choose Unit 8 Exam.
   • The proctored unit exam must be completed by the deadline date listed at the top of this page, and may be repeated under certain conditions. See the Detailed Schedule page for specific rules.

   Note: Remember that you can always go back and take practice exams on this unit after the deadline has passed. In particular, this will help you prepare for the midterm and final exams.

   • Directions: Click on the link above, then choose Unit 8 Practice Exam. After the deadline has passed, this exam will be available in practice mode.

Unit 8 Checklist

To finish Unit 8, make sure that you have completed the following items:

• Read the material listed in the Study Guidelines.
• Practice the problems listed in the Study Guidelines, and use any of the listed supplementary material to help you understand the concepts.
• Complete the online Unit Pretest (read the exam description first).
• Complete the online proctored Unit Exam.

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