Chapter 3.1 – Exponential and Logistic Functions
Chapter 3.2 – Exponential and Logistic Modeling
Chapter 3.3 – Logarithmic Functions and Their Graphs
Chapter 3.4 – Properties of Logarithmic Functions
Chapter 3.5 – Equation Solving and Modeling
Chapter 3.6 – Mathematics of Finance
Chapter 9.4 – Sequences and Series
Chapter 3 – Exponential, Logistic, and Logarithmic Functions
Chapter 9 – Discrete Mathematics (partial)
In this unit we put trigonometry aside and delve into several other topics that are major prerequisites for Calculus. Much of it will seem familiar from Algebra 2. Not only will we reinforce those older skills, but we'll also add on some new tricks. You'll develop an understanding of where exponential functions fit into real world applications. You'll then clearly understand that exponential equations such as 5x = 12 cannot be solved efficiently with any of the mathematical tools you learned prior to logarithms. Logarithms vastly expand the types of math problems we can tackle. For the sake of time we will skip Logistic functions.
After covering Chapter 3 in the textbook, finishing the year with Chapter 9.4 may seem like an abrupt change of course. But it isn't! New terminology and symbols are introduced as we get a brief intro to Sequences/Series (which get addressed much further in Calculus AB & Calculus BC). However, the underlying mathematics is very similar to linear and exponential functions, and the student who successfully makes those connections will find the content much easier to grasp.
And in case you wonder, why is this chapter taught at the end of the course, leading us to study the chapters out of order? Several reasons:
A few years ago when Physics was an 11th/12th grade course, the Physics teachers requested that I introduce trigonometry earlier in the year to better correlate with their course content. I agreed this was a good idea. Even though Physics has since been switched to a 9th grade course, I believe the new sequencing worked better for my students anyway.
Much of the current unit 4 content needs reinforcement in PreCalculus after being introduced late in the Algebra 2 year. However, I previously found that tackling it early in the year gave students the impression that PreCalculus was merely a rehash of earlier classes. I find it more effective to start the year with completely new material and then finish the year revisiting some familiar content.
I find that the current PreCalculus sequencing also leads in more logically to the AP Calculus course sequencing.
Traditionally the 4th Quarter at Lusher gets butchered with countless interruptions to our academic schedule. I find that the content of this unit 4, as I currently have it, is better able to withstand the disruptions in continuity than the trigonometry content.