Objectives (click/tap to expand)
Solve logarithmic equations algebraically
Solve exponential equations algebraically
Solve both logarithmic and exponential equations graphically
Find the domain of a logarithmic function
Solve applications: Newton's Law of Cooling
Solve applications: pH Scale
Solve applications: Richter Scale
Algebraically solving equations that include exponential or logarithmic expressions. Forgot to say it in recording the video, but I challenge you to determine what effect the 0.7 has on the population model. (Hint: Think of transformations)
Chapter 3.1 - Exponential and Logistic Functions
See assigned homework for examples of types of questions you'll be asked
Given two pairs of point coordinates (x,y), write an exponential function y = a*b^x that passes through the two points. Your book a couple of these and we've also done these as "Do Now" in class. Remember that you can make up your own points, do the task, and then easily check on calculator. Remember to use "STO."
Chapter 3.2 - Exponential and Logistic Modeling
See assigned homework for examples of types of questions you'll be asked
Chapter 3.3 - Logarithmic Functions and Their Graphs
See assigned homework for examples of types of questions you'll be asked
Chapter 3.4 - Properties of Logarithmic Functions
See assigned homework for examples of types of questions you'll be asked
"Ugly Algebra"
This "Ugly Algebra" PDF includes ten worked-out examples and seventeen exercises for you to try on your own, with answers on the last pages.
How-to videos here.
How does an object/body cool (or warm) when exposed to the steady temperature of a surrounding environment? We apply our knowledge of exponential functions and transformations to find out.
Since our book has limited exercises on the topic, here are some additional Newton's Law of Cooling exercises from other textbooks if you need the practice. Solutions included on second page.
Also, here are the extra exercises used as classwork on this class day with worked-out solutions included. Remember, there are multiple ways to solve any of these exercises.
By now we all love logarithms, right? So how about a celebratory poem...
Here are some exercises and odd answers from another PreCalculus book (Larson, 7th ed).
Go to next page, Chapter 9.4.