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4 - Exponentials and Logs

Important Concepts for This Unit

Exponential functions are used in modeling many real-world phenomena, such as the growth of a population or the growth of an investment that earns compound interest. Once an exponential model is obtained, we can use the model to predict population size or calculate the amount of an investment for any future date. To find out when a population will reach a certain level, we use the inverse functions of exponential functions, called logarithmic functions. So if we have an exponential model for population growth, we can answer questions like: When will my city be as crowded as New York City.

u4.4 Student can simplify expressions using rules of logarithms.

u4.5 Student can solve equations involving logs and exponentials.


Topic, Focus, and Exercises

 

u4.1 - EXPONENTIAL FUNCTIONS

  • The definition of an exponential function, including what it means to raise  to an irrational number.
  • The geometry of exponential functions and their transformations.

Core Exercises: 2, 12, 21, 27, 42, 49, 60

Recommended: 2, 5, 8, 12, 16, 18, 21, 26, 27, 37, 42, 46, 49, 54, 60, 65

 
   u4.2 - THE NATURAL EXPONENTIAL
  • The base e.
Core Exercises: 2, 6, 14, 19, 25

Recommended: 
2, 4, 6, 9, 14, 17, 19, 21, 25, 28, 37
 
  u4.3 LOGARITHMIC FUNCTIONS
  • Definition of the logarithm function as the inverse of the exponential function, from both a numeric and geometric perspective.
  • Properties of the logarithm function, emphasizing the natural and common logarithms.

Core Exercises: 3, 10, 15, 24, 35, 51, 58, 65, 76, 82

Recommended:
 1, 3, 4, 8, 10, 15, 19, 24, 28, 34, 35, 42, 47, 51, 54, 58, 60, 65, 76, 82, 94, 99, 102
 
  u4.4 LAWS OF LOGARITHMS
  • The laws of logarithms, including the change of base formula.
Core Exercises: 5, 19, 32, 47, 52, 57, 67, 72

Recommended: 3, 5, 10, 15, 19, 25, 32, 44, 47, 49, 52, 55, 57, 63, 67, 71, 72, 76




 
  u4.5 EXPONENTIAL AND LOGARITHMIC EQUATIONS
  • Solving equations involving exponential and logarithmic functions, algebraically and graphically.

Core Exercises: 4, 12, 36, 47, 53, 59, 81, 88, 98

Recommended: 1, 4, 10, 12, 22, 30, 36, 40, 47, 50, 53, 59, 72, 78, 81, 84, 88, 94, 98, 105

 
 u4.6 MODELING WITH EXPONENTIAL FUNCTIONS

  • Translating verbal descriptions of problems into mathematical models, and solving the problems using the models.
  • Certain standard types of problems such as those dealing with exponential growth and decay.

Core Exercises: 3, 12, 25

Recommended: 3, 6, 10, 12, 16, 21, 25, 27


  
u4.7 LOGARITHMIC SCALES

  • Translating verbal descriptions of problems into mathematical models, and solving the problems using the models.
  • Certain standard types of problems such as those dealing with logarithmic scales.

Core Exercises: 6, 13, 21

Recommended: 2, 6, 9, 13, 17, 20, 21





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Nikhil Joshi,
May 16, 2017, 9:29 AM
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Nikhil Joshi,
Mar 14, 2017, 7:12 AM
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Mar 14, 2017, 7:12 AM
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Nikhil Joshi,
Mar 14, 2017, 7:16 AM
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Nikhil Joshi,
May 3, 2017, 12:57 PM
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Nikhil Joshi,
Mar 14, 2017, 7:16 AM