Lesson 19 | Exponents and Exponential Functions | 9th Grade Mathematics

Objective

Write exponential growth functions to model financial applications, including compound interest.

Common Core Standards

Core Standards

The core standards covered in this lesson

F.IF.C.8.B — Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01 ^12t, y = (1.2)^t/10, and classify them as representing exponential growth or decay.

Interpreting Functions

F.IF.C.8.B — Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01 12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.

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).

Linear, Quadratic, and Exponential Models

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.

Linear, Quadratic, and Exponential Models

F.LE.B.5 — Interpret the parameters in a linear or exponential function in terms of a context.

Foundational Standards

The foundational standards covered in this lesson

7.RP.A.3

Ratios and Proportional Relationships

7.RP.A.3 — Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Identify the percent change in exponential growth functions.
Understand the difference between simple interest (linear growth) and compound interest (exponential growth).
Understand that where compounding happens more frequently, the growth rate will be higher.
Write and evaluate exponential functions for compound interest situations and compare to simple interest situations.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

Act 1:

a. Watch the video of Act 1 of “Fry’s Bank.”

b. How much money do you think Fry has in his bank account now? Make a guess that is too low. Make a guess that is too high.

Act 2:

c. What information do you need to know about Fry’s account to determine exactly how much he has in his account now?

Act 3:

d. Watch the video of Act 3.

e. Are you surprised?

f. Do you think Fry’s account earned interest in a linear growth model or an exponential growth model?

g. What equation do you think models this?

Guiding Questions

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References

Dan Meyer's Three-Act Math Fry's Bank

Fry's Bank by Dan Meyer is licensed under the CC BY 3.0 license. Accessed May 17, 2018, 1:16 p.m..

Problem 2

Consider the three situations below.

Situation A: You invest $1,000 for 5 years at a simple annual interest rate of 4.8%.

Situation B: You invest $1,000 for 5 years at an interest rate of 4.8% compounded annually.

Situation C: You invest $1,000 for 5 years at an interest rate of 4.8% compounded monthly.

a. Determine how much money you would have in your account in each situation. Assume you make neither deposits nor withdrawals.

b. Determine how much you would have in your account in each situation if you invested for 25 years instead of 5 years.

c. Under what circumstances will your investment earn the most interest?

Guiding Questions

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

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

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

1. A youth group has a yard sale to raise money for a charity. The group earns $800 but decides to put its money in the bank for a while. The group considers two different banks:

Cool Bank pays simple interest at a rate of 4%, and the youth group plans to leave the money in the bank for 3 years.
Hot Bank pays an interest rate of 3% compounded annually, and the youth group plans to leave the money in the bank for 5 years.

Write a function to represent the amount of money earned at each bank. Then determine how much money the youth group would earn in each situation.

2. If the youth group needs the money quickly, which is the better choice? Explain your reasoning.

References

EngageNY Mathematics Algebra I > Module 3 > Topic A > Lesson 4 — Exit Ticket

Algebra I > Module 3 > Topic A > Lesson 4 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.

EngageNY Mathematics Algebra I > Module 3 > Topic A > Lesson 4 — Problem Set
MARS Formative Assessment Lessons for High School Representing Linear and Exponential Growth
Illustrative Mathematics A Valuable Quarter
Mathematics Vision Project: Secondary Mathematics Two Module 2: Linear & Exponential Functions — 2.5 "Half-Interested", 2.6 "More Interesting"

Lesson 18

Lesson 20

Lesson Map

Topic A: Exponent Rules, Expressions, and Radicals

Use exponent rules to analyze and rewrite expressions with non-negative exponents.

8.EE.A.1

Add and subtract polynomial expressions using properties of operations.

A.APR.A.1

Multiply polynomials using properties of exponents and properties of operations.

A.APR.A.1

Solve mathematical applications of exponential expressions.

8.EE.A.1

Use negative exponent rules to analyze and rewrite exponential expressions.

8.EE.A.1 A.SSE.A.2

Define rational exponents and convert between rational exponents and roots.

N.RN.A.1 N.RN.A.2

Write equivalent radical and rational exponent expressions. Identify quantities as rational or irrational.

N.RN.B.3

Simplify radical expressions.

N.RN.A.2

Multiply and divide rational exponent expressions and radical expressions.

N.RN.A.2 N.RN.B.3

Add and subtract rational exponent expressions and radical expressions.

N.RN.A.2 N.RN.B.3

Topic B: Arithmetic and Geometric Sequences

Describe and analyze sequences given their recursive formulas.

F.BF.A.2 F.IF.A.2 F.IF.A.3

Write recursive formulas for sequences, including the Fibonacci sequence.

F.BF.A.2 F.IF.A.2 F.IF.A.3

Define arithmetic and geometric sequences, and identify common ratios and common differences in sequences.

F.BF.A.2 F.LE.A.2

Write explicit rules for arithmetic sequences and translate between explicit and recursive formulas.

F.BF.A.2 F.IF.A.3 F.LE.A.2

Write explicit rules for geometric sequences and translate between explicit and recursive formulas.

F.BF.A.2 F.IF.A.3 F.LE.A.2

Topic C: Exponential Growth and Decay

Compare rates of change in linear and exponential functions shown as equations, graphs, and situations.

A.SSE.A.1 F.IF.C.9 F.LE.A.1 F.LE.A.3

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

A.SSE.A.1 F.LE.A.1 F.LE.A.2 F.LE.B.5

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

F.BF.B.3 F.IF.C.7.E

Write exponential growth functions to model financial applications, including compound interest.

F.IF.C.8.B F.LE.A.2 F.LE.B.5

Write, graph, and evaluate exponential decay functions.

F.BF.B.3 F.IF.C.7.E F.IF.C.8.B F.LE.A.1.C

Identify features of exponential decay in real-world problems.

F.IF.C.8.B F.LE.A.1.C

Solve exponential growth and exponential decay application problems.

F.IF.C.8.B F.LE.A.1 F.LE.A.2

Exponents and Exponential Functions

Objective

Common Core Standards

Core Standards

Interpreting Functions

Linear, Quadratic, and Exponential Models

Linear, Quadratic, and Exponential Models

Foundational Standards

Ratios and Proportional Relationships

Criteria for Success

Anchor Problems

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem Set

Target Task

References

Additional Practice

Lesson Map

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