Curriculum / Math / 11th Grade / Unit 5: Exponential Modeling and Logarithms / Lesson 3
Math
Unit 5
11th Grade
Lesson 3 of 16
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Write and change the form of exponential functions that model compounding interest.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
F.LE.A.1.A — Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
F.LE.A.1.B — Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
F.LE.A.1.C — Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Below are two good articles to read before teaching this lesson:
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
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.
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..
You put $500 in a savings account that advertises 5% interest.
Which bank will yield more money after 10 years?
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.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
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.
Which rate will make the most in interest over a given period of time?
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.
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.
Lesson 2
Lesson 4
Topic A: Modeling with and Interpreting Exponential Functions
Identify, model, and analyze geometric sequences.
F.IF.A.3 F.IF.B.5 F.LE.A.2
Analyze and construct exponential functions that model contexts.
F.IF.B.4 F.IF.C.8.B F.LE.A.2
F.BF.A.1.A F.LE.B.5
Define and use $$e$$ in continuous compounding situations.
A.SSE.B.3.C F.BF.A.1.A
Describe the derivation of the formula for the sum of a finite geometric series and use it to solve problems.
A.SSE.B.4
Find the sum of an infinite geometric series.
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Topic B: Definition and Meaning of Logarithms
Describe and evaluate simple numeric logarithms (Part I).
F.LE.A.4
Describe and evaluate simple numeric logarithms (Part II).
Describe logarithms as the inverse of exponential functions and graph logarithmic functions.
F.BF.B.3 F.BF.B.4.B F.BF.B.4.C F.BF.B.5 F.IF.C.7.E
Evaluate common and natural logs using tables, graphs, and calculators.
F.BF.B.4.C F.LE.A.4
Understand and apply the change of base property to evaluate logarithms.
Develop and use the product and quotient properties of logarithms to write equivalent expressions.
Develop and use the power property of logarithms to write equivalent expressions.
F.BF.B.4.B F.LE.A.4
Solve equations with logarithms.
Use logarithms to solve exponential modeling problems (Part I).
A.SSE.A.1.B F.LE.A.4
Use logarithms to solve exponential modeling problems (Part II).
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