Log inSign up for FREE
Library

5.2 Exploring Expontential Growth

Last updated 10 months ago
19 questions
Note from the author:
OBJECTIVES & STANDARDS
Math Objectives
  • Recognize that exponential patterns grow by a constant growth factor
  • Distinguish between exponential and linear functions
Common Core Math Standards
  • Link to all CCSS Math
  • CCSS.PRACTICE.MP4
  • CCSS.HSF.LE.A.1
  • CCSS.HSF.LE.A.1.A
  • CCSS.HSF.LE.A.3
Personal Finance Objectives
  • Recognize that investments grow exponentially
National Standards for Personal Financial Education
Investing
  • 4a: Describe the impact of inflation on prices over time
  • 4b: Explain the relationship between nominal and real returns.
  • 8-5a: Explain the benefit of compound interest as compared with simple interest.
DISTRIBUTION & PLANNING
Distribute to students
  • Student Activity Packet
  • Application Problems
  • Visual Pattern Cards
OBJECTIVES & STANDARDS
Math Objectives
  • Recognize that exponential patterns grow by a constant growth factor
  • Distinguish between exponential and linear functions
Common Core Math Standards
  • Link to all CCSS Math
  • CCSS.PRACTICE.MP4
  • CCSS.HSF.LE.A.1
  • CCSS.HSF.LE.A.1.A
  • CCSS.HSF.LE.A.3
Personal Finance Objectives
  • Recognize that investments grow exponentially
National Standards for Personal Financial Education
Investing
  • 4a: Describe the impact of inflation on prices over time
  • 4b: Explain the relationship between nominal and real returns.
  • 8-5a: Explain the benefit of compound interest as compared with simple interest.
DISTRIBUTION & PLANNING
Distribute to students
  • Student Activity Packet
  • Application Problems
  • Visual Pattern Cards
Intro/Warm-Up
COMPARE: Which One Doesn’t Belong?
Study the tables below to identify patterns, similarities, and differences. Then, answer the question.

4
What do you notice about the tables?_______ Identify 3 similarities or differences between them.
1. _______
2. _______
3. _______
1

Which table doesn’t belong? Explain your reasoning.

Explore It
MOVE: Exponential Growth
Follow your teacher’s instructions to complete this activity. Then, answer the questions.
1

In Round 1, how many people stood up with each tap?

1

In Round 2, how many people stood up with each tap?

1

Which round did you complete the fastest? Explain why you think that was the case.

1

Do you think the results would have been different if you did this with a stadium full of people? Why or why not?

Learn It
DESMOS#1: Exponential Growth in Circles
You’ve seen how exponential growth can happen quickly. Next, you’ll explore an exponential function in more detail, with both a visual pattern and numbers, to learn how to measure its growth. Follow your teacher’s instructions to complete this Desmos activity.
Practice It
Now that you’re familiar with exponential patterns, you’ll explore their different representations with your group. It’s okay if some parts seem new or confusing; it might take some work to figure out. Follow your teacher’s instructions to complete this activity.
CREATE: Exponential Patterns Jigsaw
Let’s explore exponential change using visual patterns. Exponential change happens when you have a starting value that you repeatedly multiply by a certain value, called the growth factor. In this activity, you’ll work with your group to understand one visual exponential pattern and represent it in different ways.

Part I: Explore Your Pattern

Your teacher will assign you to a group to work on one of the Visual Pattern Cards. Work with your group to complete the table below based on your assigned pattern.
0

Draw a representation of the next step in the pattern. If the next step has too many pieces, you can draw a partial representation and explain what the complete step would look like.

0

Describe the way you see the pattern increasing or decreasing. Be sure to identify the growth factor and explain what that means in your pattern.
Note: for Pattern D, it will be called the decay factor.

0

Create a table representing the pattern with numbers. (draw it in show your work if that is easier)

0

Plot the points from the table on the graph to illustrate the pattern. ( you may also screen shot a desmos with the points in the show your work)

  • Click the graph tab.
  • Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.
Which pattern do you think would have the largest y value when x = 20? Explain your reasoning.
Learn It & Practice It
Desmos #2 Exponential vs Linear Patterns (Financial Algebra 5.2)
COMPARE: Exponential vs Linear Patterns
Now that you’ve explored exponential growth, consider how it compares to linear growth.
Application Problems
Level 1: Desmos #3: Growth Factor and Investments (Financial Algebra 5.2)
Level 2:
The graph below represents the value of Lucas’ investments, which average 8% annual returns.

5
a. What was the initial balance in the account?_______
b. Approximately how much did the value of Lucas’ investments increase in the first 10 years?_______
c. Is the account growing by the same number of dollars each year? Explain how you know._______
5
At the same time as Lucas, Mikal decides to start saving with an initial deposit of $500 as well. His account doesn’t earn any interest, but he is consistent about making annual deposits.

a. How much does Mikhal need to save each year to have the same amount as Lucas after approximately 30 years?around $_______

b. How much more did Mikhal end up depositing in total than Lucas?$_______

c. Graph Mikhal’s account balance on the same coordinate plane. (screen shot graph in show your work)

d. How does the growth of the two account balances compare?_______
1
The table below represents the growth of an investment account over 3 decades.


What is the growth factor of this function?_______
2
The table below represents the growth of an investment account over 4 years.


What is the growth factor of this function?_______
Level 3:
0
Part 1: Growth Factor
The table below represents the growth of an investment account over 5 years. Complete the table and answer the questions.

a. What is the growth factor of this function?_______

b. What is the annual rate of return in this account? Hint: By what percentage does this function increase each year?_______ %

c. What was the initial value in the investment account?$_______
0

The table below represents the value of an investment account, y, after x years.


Which of the equations options do you think represents the account’s growth? Justify your response using math terms from this lesson.

0
Imagine an item that costs $300 today (like 3 concert tickets or a nice winter jacket). The graph below represents the change in the price of that item over time, assuming an average annual inflation rate of 2%.

a. Approximately how much has the price of the item increased after 15 years?$_______
b. This function has a growth factor of 1.02 and is exponential. Why does it appear almost linear in the graph?_______
c. This function shows a 2% annual increase in price, using the equation y = 300(1.02)x. Rewrite this equation to instead show the 2% annual decrease in purchasing power of that same $300 over time._______
0
Hadley puts $300 in a savings account earning 1% annual interest and $300 in an investment account that averages 5% annual returns. The graph below shows the balance in those accounts over 20 years. The dashed line reflects the change in price of a $300 item due to 2% annual inflation.

Approximately how much has Hadley’s initial investment grown over 20 years? Include both the dollar value $_______ and percent change (return on investment)._______ %
0
The real rate of return on an investment is the annual rate of return after taking into account the impacts of inflation. It more accurately reflects the purchasing power of your money. You can calculate it using the formula below, where “nominal rate” is the given rate of return.

a. What is the real rate of return on Hadley’s investments? Refer back to question 18._______ %
b. What is the real rate of return on Hadley’s savings?_______ %
c. How does the graph show the impact of inflation on the value of Hadley’s savings over time?_______
d. Question 4 used the equations
to represent Hadley’s savings and investment balances over time, respectively. Rewrite these equations to represent their account balances based on their real rate of return.
Invetments: _______
Savings: _______