Lesson 6: Graphs and applications of exponential and logarithmic functions

Learning Goals

At the end of the lesson, students will be able to...

• Understand and use different methods for solving equations involving indices using logarithms

• Understand the effects and transformations of exponential and logarithmic fucntions

LESSON STRUCTURE

1. Introduction (10 minutes) - Revision activity

2. Body Activity 1 (10 minutes) - Information gap actiivity (AFL) (LIT)

3. Body Activity 2 (5 minutes) - A look at a real exponential graph

4. Body Activity 3 (25 minutes) - Class exploration of transformations (LIT)

5. Conclusion (5 minutes) - Making connections (AFL)

Duration: 10 minutes

Activity Description

The purpose of this activity is to remind students of the two methods used to solve equations involving indices using logarithms, which was practiced in earlier class

Teacher Action

• Teacher will remind students of the two methods

• Teacher will do example on board to remind students

• Teacher will also instruct students to write down methods and use calculator to evaluate final expression

• Teacher will make sure all students know how to use calculator and input values correctly

Student Action

• Students will participate in discussion about methods for solving equations

• Students will write down methods and practice using calculator to find answer

Sample of methods to be taught

Duration: 10 minutes

Resources

Past exam questions

Activity Description

The purpose of this activity is to reinforce the skills and methods they have already learned regarding this concept and apply the different methods. Students will be put into pairs and be given past exam questions, where one student will solve it with one method and the other students with the second method. They will then come together to explain how they have done the question with their method. This activity also helps students apply their understanding of the methods and solidify their understanding of the methods.

Teacher Action

• Teacher get students into pairs and provide past exam questions

• Teacher asks students to complete questions

• Teacher will ask students to share with partner how they used method

• Teacher will monitor students and make sure any misunderstandings are addressed and help any students who are struggling

Student Action

• Students will practice completing questions

• Students will share their understanding of method to partner

Duration: 5 minutes

Resources

https://www.nytimes.com/2021/05/14/learning/the-math-of-ending-the-pandemic-exponential-growth-and-decay.html

Activity Description

The purpose of this activity is to show students an example of a real-life exponential graph based on the exponential growth of Covid-19. This activity will engage students due to its recent relevancy, and will also scaffold students for the assessment which involves looking at data of exponential graphs and linking it to their knowledge of logarithmic and exponential functions. The end of this lesson will also call back on this data and graph to help start students develop their understanding of the connection between the functions and real-life examples.

Teacher Action

• Teacher will present exponential graph of Covid-19 pandemic

• Teacher will briefly explain graph and cases and answer any questions students have about the graph, data, and curve

Student Action

• Students will ask questions they might have

• Students will look at exponential graph

Duration: 25 minutes

Resources

Desmos: https://www.desmos.com/calculator

Activity Description

The purpose of this activity is to allow students to engage in an exploration in groups to explore the effect of changing the values k, b, and c on the graphs of y=ka^x+c and y=ka^(x+b). Students will use graphing software Desmos in groups to explore changing different aspects or values and understand how they affect the exponential graph. This activity gives students an understanding of how to sketch these different types of exponential graphs by hand. Getting students to investigate in groups and then stand in front of class to teach what they explored and found to other students is engaging and allows students listening to learn from other students about what they explored.

Teacher Action

• Teacher will get students into groups and give them a group of functions to graph and explore and look at how changing a value affects the graph

• Teacher will tell students they will be teaching what they explore to rest of class in discussion towards end

• Teacher will remind students of language to use in their discussion

• Teacher will monitor students and make sure that they are coming to insights with their explorations but that they also are correctly understanding their group of functions

Student Action

• Students will participate in exploration in groups

• Students will work on how they will teach their exploration to rest of class

Group of functions

Duration: 5 minutes

Activity Description

The purpose of this activity is to get students to understand and make connections between their exploration and the real exponential graph looked at earlier in lesson. This is to see what connections students have made about their investigations on changing values and how this relates to the real life exponential graph, and if students are lacking in a certain understanding or connection overall this can be addressed in the next lesson.

Teacher Action

• Teacher will ask students to write down on a piece of paper what they learned in exploration and discussion about the effect of changing values and how this relates to real exponential graphs

• Teacher asks students to hand in piece of paper when done

Student Action

• Students will participate in activity