1.4: Connecting Growth Factor to Percent Change

1.4 Connecting Growth Factor to Percent Change

LEARNING OBJECTIVES

1.1.3 Construct a representation of a linear,

quadratic, or exponential function both with and without technology.

1.1.4 Use a function that models a data set or

contextual scenario to predict values of the dependent variable.

Open Ended

Warm-up #1

What are some of the key features of exponential functions? Look back at the vocabulary graphic organizer for exponential functions that you made in Lesson 1.1 if you need help remembering.

Open Ended

Warm-up #2

What does the graph of an exponential function look like?

Open Ended

Warm-up #3

How are linear and exponential functions similar and how are they different?

Answer to Warm up Question #1

Answer to Warm up Question #2

Answer to Warm up Question #3

Student Task

Open Ended

Question to consider while building your table.

#1

• What is the initial value of the car?

Open Ended

Question to consider while building your table.

#2

• Can we model this scenario with a function? Why or why not?

Open Ended

Question to consider while building your table.

#3

• By how much does the value of the car decrease every year? Is that amount constant or does it change?

Open Ended

Question to consider while building your table.

#4

• After one year, what is the value of the car? How can that be calculated?

Complete your Table

Here are your table headings

Your completed table should look something like this

Open Ended

Summarizing the Task

#1

1. What are the independent and dependent variables for this scenario?

Open Ended

Summarizing the Task

#2

1. If the value of the car decreases by 20%, why is the decay factor 0.8?

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Summarizing the Task

#3

1. Use the algebraic representation of the function to confirm that the value of the car after 10 years is $1,932.74, which is equal to what you determined in your table of values.

Summarizing the Task Answers

Part 2: Writing a Function Model with Two Data Pairs

Handout 1.4: Modeling the Value of a Classic Car.
This can be found in your work books

Things to Consider while working on the 1.4 Handout

• What two quantities are being related in this scenario? What could we identify as the independent and dependent variables?

• What are the two data pairs given in the scenario?

• Consider the units for the independent and dependent variables. What does the slope of the line mean in the context of the problem?

• Is the percent change an increase or a decrease? How do you know?

• Is the percent change an increase or a decrease? How do you know?

Open Ended

Things to Consider while working on the 1.4 Handout

#1

• What two quantities are being related in this scenario? What could we identify as the independent and dependent variables?

Open Ended

Things to Consider while working on the 1.4 Handout

#2

• What are the two data pairs given in the scenario?

Open Ended

Things to Consider while working on the 1.4 Handout

#3

• Consider the units for the independent and dependent variables. What does the slope of the line mean in the context of the problem?

Open Ended

Things to Consider while working on the 1.4 Handout

#4

• Is the percent change an increase or a decrease? How do you know?

​Answers to Things to Consider for 1.4 Handout

Open Ended

Things to Consider while working on the 1.4 Handout

#5

• How could we use the given information to determine the growth factor and the

  percent change over five years?

Complete 1.4 Handout

​1.4 Handout Answers

Work through the reasoning for how to use the growth factor over five years to determine the growth factor per year.

Open Ended

What are your thoughts?

#1

1. If the growth factor over one year is about 1.15, what is the percent increase in the value of the car over one year? How do you know?

Open Ended

What are your thoughts?

#2

1. Write an exponential function model to estimate the average value of a first-generation Bronco in 2021.

What are your thoughts?
Possible answers

Part 3: Understanding Compounding Interest

You want to buy a new computer for $1,500 from Computer SuperStore. Since you

don’t actually have $1,500 for the computer, you decide to apply for a store credit card.

When a person makes a purchase with a credit card, they are often charged interest.

Interest is a fee charged in exchange for allowing you to borrow money and is usually

calculated as a percent of the balance you owe. There are three different credit cards

available at Computer SuperStore:

Option 1: Interest charged 24% annually

Option 2: Interest charged 6% quarterly

Option 3: Interest charged 2% monthly

Complete a table of values for each option. Then justify which option you would

choose using a mathematical argument involving exponential functions.

​Student Task

​Create a table for 1 full year
Here is a start... at the end also create an algebraic representation for each function

​Your completed table might look like this

Open Ended

Summarizing the Task

Which option would you select and why?

​Thoughts that might have come up in Summarizing the task

Take away:
Compound Interest Formula

​Complete the Assess and Reflect on the Lesson

You can now complete the printed copy of the 1.4 Formative Assessment.
Please see the teacher for your copy.