Exponential Modeling and Logarithms

Lesson 3

Math

Unit 5

11th Grade

Lesson 3 of 16

Objective


Write and change the form of exponential functions that model compounding interest.

Common Core Standards


Core Standards

  • F.BF.A.1.A — Determine an explicit expression, a recursive process, or steps for calculation from a context.
  • F.LE.B.5 — Interpret the parameters in a linear or exponential function in terms of a context.

Foundational Standards

  • F.LE.A.1.A
  • F.LE.A.1.B
  • F.LE.A.1.C

Criteria for Success


  1. Identify the components of compounding interest functions and relate them to a context.
  2. Write compounding interest functions.
  3. Identify the effective percentage rate from compounding interest functions.

Tips for Teachers


Below are two good articles to read before teaching this lesson:

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Anchor Problems

25-30 minutes


Problem 1

Suppose that water is entering a cylindrical water tank so that the initial height of the water is $$3$$ cm and the height of the water doubles every $$30$$ seconds. Write an equation of the height of the water at time $$t$$ seconds.

Guiding Questions

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References

EngageNY Mathematics Algebra II > Module 3 > Topic A > Lesson 6Exit Ticket, Question #1

Algebra II > Module 3 > Topic A > Lesson 6 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..

Problem 2

You put $500 in a savings account that advertises 5% interest. 

  • Bank A pays interest once a year, and the interest model is $${B=500(1.05)^t}$$, where $$B$$ is the balance in the account after $$t$$ years. 
  • Bank B pays interest monthly, and the interest model is $$B=500(1+{.05\over12})^{12t}$$, where $$B$$ is the balance in the account after $$t$$ years.

Which bank will yield more money after 10 years? 

Guiding Questions

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

References

Illustrative Mathematics The Bank Account

The Bank Account, accessed on Feb. 22, 2018, 2:49 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.

Modified by Fishtank Learning, Inc.

Target Task

5-10 minutes


A man invests $1,000 in an account with a 5% annual percentage rate.

Write equations that model the balance in the account, $$B$$, if the interest is compounded at the following rates in $$t$$ years. 

  • Semi-annually
  • Quarterly
  • Monthly
  • Daily 

Which rate will make the most in interest over a given period of time?

References

Illustrative Mathematics Compounding with a 5% Interest Rate

Compounding with a 5% Interest Rate, accessed on Feb. 22, 2018, 2:57 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.

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.

  • Include problems making comparisons—for instance, “Which is better, 3% compounded annually or 2.5% compounded monthly?” 
  • Include problems writing equations from tables.

Next

Define and use $$e$$ in continuous compounding situations.

Lesson 4
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Lesson Map

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

Topic A: Modeling with and Interpreting Exponential Functions

Topic B: Definition and Meaning of Logarithms

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