Lesson 20: Exponential and Logarithmic Functions

Preview

Here's the on-ramp for this lesson.


What Will We Learn?

  • The first 19 lessons in this course developed the concepts of calculus in the context of algebraic functions. This lesson marks the start our journey back through all the calculus concepts we've learned -- limits, differentiation, integration -- but this time in the context of transcendental functions. This lesson focuses on reviewing exponential and logarithmic functions.


Why Do We Need to Learn This?

  • Though we've learned all the essential elements of calculus already over the past 19 lessons in this course, we've only done so for algebraic functions. Many, many real-world applications of mathematics involve exponential and logarithmic functions -- see below for a list of examples -- and so to have both a broader understanding of calculus and a greater range of potential real-world applicability we will want to learn about the calculus of exponential and logarithmic functions.

Review

Learn

The lesson notes below contain a learning plan with three stages -- Learn, Reflect, and Practice -- and guidance for what to do within each stage. Some tips for you as you work through this resource, and those that it points to:

  • I recommend using Cornell Notes (or a modification of it; see this video starting at the 1:05 mark) to take notes on the lesson and the videos. This note-taking method balances detail with big-picture thinking to help you summarize and retain what you are learning. See this other video for additional note-taking techniques you might want to experiment with.

Lesson Notes

Lesson 20.pdf

Video 1 (Example B.11)

Video 2 (Example B.11)

Reflect

If you are currently enrolled in this course with me, submit the written reflections Google Form I have emailed you after working through the lesson notes and videos. Some tips:

  • Submit substantive, but concise, answers to each question; you will be doing the future you a big favor by taking time now to accurately and succinctly summarize what you have learned from the lesson.

  • Send yourself a copy of your reflections; they will come in handy later when you start preparing for quizzes and other assessments.

If you are not currently enrolled in this course with me, those written reflections ask three reflective questions designed to help you retain what you've learned and pinpoint any remaining areas of confusion. Those questions are:

  • Please summarize the main mathematical takeaways from the lesson notes.

  • What was the most interesting part of what you learned, and why?

  • What, if anything, do you still find confusing?

Practice

Work through the practice problems suggested below to see how much of this lesson you've understood.

Lesson 20 PP.pdf