Curriculum  /  Math  /  9th Grade  /  Unit 6: Exponents and Exponential Functions  /  Lesson 17

Exponents and Exponential Functions

Lesson 17

Math

Unit 6

9th Grade

Lesson 17 of 22

Objective

Write linear and exponential models for real-world and mathematical problems.

Common Core Standards

Core Standards

  • F.LE.A.1 — Distinguish between situations that can be modeled with linear functions and with exponential functions.
  • F.LE.A.2 — Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
  • F.LE.B.5 — Interpret the parameters in a linear or exponential function in terms of a context.
  • A.SSE.A.1 — Interpret expressions that represent a quantity in terms of its context Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.

Foundational Standards

  • 8.F.A.3
  • 8.F.B.4

Criteria for Success

  1. Identify features of linear and exponential functions in contextual situations. 
  2. Write linear and exponential functions for real-world situations. 
  3. Write linear and exponential functions from two input-output pairs.
Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes

Problem 1

For each of the scenarios below, decide whether the situation can be modeled by a linear function, an exponential function, or neither. For those with a linear or exponential model, create a function that accurately describes the situation.

  1. From 1910 until 2010, the growth rate of the United States has been steady at about 1.5% per year. The population in 1910 was about 92,000,000.  
  2. The circumference of a circle as a function of the radius
  3. According to an old legend, an Indian King played a game of chess with a traveling sage on a beautiful hand-made chessboard. The sage requested, as reward for winning the game, one grain of rice for the first square, two grains for the second, four grains for the third, and so on for the whole chess board. How many grains of rice would the sage win for the $${n^{th}}$$ square?
  4. The volume of a cube as a function of its side length  

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Illustrative Mathematics Finding Linear and Exponential Models

Finding Linear and Exponential Models, accessed on May 17, 2018, 12:49 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 2

The population of a country is initially 2 million people and is increasing at 4% per year. The country's annual food supply is initially adequate for 4 million people and is increasing at a constant rate adequate for an additional 0.5 million people per year.

  1. Based on these assumptions, in approximately what year will this country first experience shortages of food?
  2. If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for an additional 0.5 million people per year, would shortages still occur? In approximately which year?
  3. If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Illustrative Mathematics Population and Food Supply

Population and Food Supply, accessed on May 17, 2018, 12:50 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem 3

Two points are shown below.

$${A (1,6)}$$

$${B (0,2)}$$

  1. Write a linear function that contains these two points. 
  2. Write an exponential function that contains these two points.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

Chain emails are emails with a message suggesting you will have good luck if you forward the email on to others. Suppose a student started a chain email by sending the message to 3 friends and asking those friends to each send the same email to 3 more friends exactly 1 day after receiving it. 

  1. Write a function to represent the number of people who receive the email on the $${n^{th}}$$ day. Assume everyone who receives the email follows the directions. 
  2. Did you write an exponential function or a linear function? Explain your reasoning behind your decision. 
  3. Which day is the first day that the number of people receiving the email exceeds 100?

References

EngageNY Mathematics Algebra I > Module 3 > Topic A > Lesson 5 — Exit Ticket

Algebra I > Module 3 > Topic A > Lesson 5 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Next

Graph exponential growth functions and write exponential growth functions from graphs.

Lesson 18
icon/arrow/right/large

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Exponent Rules, Expressions, and Radicals

Topic B: Arithmetic and Geometric Sequences

Topic C: Exponential Growth and Decay

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free