Unit 5: Exponential and Logarithmic Functions

5.1 Exponential Functions

Video 1: Introduction to exponential functions.

Video 2: Approximating exponential expressions with base 2 as exponentials with base 10.

Video 3: What to do with irrational inputs to exponential functions.

 Assignment 5.1:

  • p.334: #1,2,3-11 odd, 12-16 all, 17-31 odd, 43,45,46,49-52 all

 

5.2 Tangent lines, instantaneous rates of change and the number e.

Video 4: Tangent Lines

Video 5: Instantaneous Rate of Change

Video 5: The number e

Assignment 5.2:

  • p.342: #11-20 all. (I know that seems like a lot, but it should go fast…unless you really need the practice),23,25,26,27 (feel free to write some code that fills out the tables for you), 43,45,49,51,55,61

 

5.3 Logarithmic Functions

Video 6: Introduction to the logarithmic function

Video 7: The graph of a logarithmic function

Assignment 5.3:

  • p.356; #1-4 all
  • p.356; Make sure you know how to do these (Optional inverse function review): #6,7,8
  • p.357; 9,11
  • Do these without a calculator: 15-18 all
  • p.357; 19,21,23,24,25,43,45,47,49,51,65
  • Honors: Write a program that fills out the charts for #68, also #69 (no code for this one)

 

(Open note) Possible quiz topics for wednesday:

  • Basic questions about functions and their inverses. You may want to go back to the unit on functions for review.
  • What does it mean for a function to be one to one?
  • Why does the horizontal line test work?
  • Explain how video 5 defines the number e.
  • Give a verbal description of the meaning of the log of a number with a given base.
  • Convert equations from logarithmic form to exponential form and visa versa.
  • Sketch the graphs of exponential and logarithmic functions on the same axes. Describe their domains and ranges.

5.4 Tangent lines, instantaneous rates of change and the number e.

Video 8: Properties of logarithms


 

Video 9: more properties of logarithms

Video 10: Properties of logarithms examples.

Assignment 5.4:

  • p.368; #1-17 odd, 21-27 odd
  • p.369; #51,52,51,55 (I know this seems out of order)
  • p.369; #31,33 (You might want to do 51-55 first, to get a little practice with change of base.)
  • p.369; #43,45,47
  • p.369; #62 (If you are working in a group, make sure that everyone comes up with their own examples.)
  • p.369; #63

5.5 Solving Equations Involving Exponential Functions and Logarithms

Video 10: Solving equations with variables in exponents

Video 11: More solving equations with variables in exponents

Assignment 5.6:

  • p.380; #1-25 every other odd
  • p.381; #45-49 odd
  • 5.6 Compound Interest



    Assignment 5.5:

    • p.391; #1-19 every other odd
    • p.391; #21, ,23(see #22 a for a hint),25,27,
    • Honors: Project on page 392