Students revisit exponential functions, including geometric sequences and series, and learn to manipulate logarithmic expressions and equations to solve problems involving exponential modeling.
Students have previously seen exponential functions in Algebra I. This unit builds off of that knowledge, revisiting exponential functions and including geometric sequences and series and continuous compounding situations. In the second part of the unit, students learn that the logarithm is the inverse of the exponent and to manipulate logarithmic expressions and equations. Finally, students apply their knowledge of logarithms to solve problems involving exponential modeling.
This unit is an excellent opportunity for students to practice mathematical modeling using exponential functions as models for situations in the world. Students will also look for and make use of structure as they manipulate logarithms and connect their knowledge of exponents to logarithms.
While this unit culminates the study of exponents and logarithms in the Common Core State Standards, it leads to essential topics in calculus. Students preparing to take a calculus course should emphasize algebraic manipulation of exponential and logarithmic expressions to rewrite them in a variety of ways, including using properties of logarithms and analyzing functions to connect their graphs to equations and contextual situations.
This assessment accompanies Unit 5 and should be given on the suggested assessment day or after completing the unit.
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Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
Unit-Specific Intellectual Prep
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Geometric sequence | Geometric series |
Compounding/Continuous compounding | Percentage Rate |
e (Euler's number) | Base |
Rate | Argument |
Principal | Finite geometric series |
Sum of geometric series | Summation notation $${\sum}$$ |
Logarithm | Natural log |
Common log | Change of base |
Product property of logarithms (Logarithm law) | Quotient property (Logarithm law) |
Power property (Logarithm law) | Exponentiate |
Exponential growth | Exponential decay |
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F.IF.A.3
F.IF.B.5
F.LE.A.2
Identify, model, and analyze geometric sequences.
F.IF.B.4
F.LE.A.2
F.IF.C.8.B
Analyze and construct exponential functions that model contexts.
F.LE.B.5
F.BF.A.1.A
Write and change the form of exponential functions that model compounding interest.
A.SSE.B.3.C
F.BF.A.1.A
Define and use $$e$$ in continuous compounding situations.
A.SSE.B.4
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.
F.LE.A.4
Describe and evaluate simple numeric logarithms (Part I).
F.LE.A.4
Describe and evaluate simple numeric logarithms (Part II).
F.BF.B.3
F.BF.B.5
F.IF.C.7.E
F.BF.B.4.B
F.BF.B.4.C
Describe logarithms as the inverse of exponential functions and graph logarithmic functions.
F.LE.A.4
F.BF.B.4.C
Evaluate common and natural logs using tables, graphs, and calculators.
F.LE.A.4
Understand and apply the change of base property to evaluate logarithms.
F.LE.A.4
Develop and use the product and quotient properties of logarithms to write equivalent expressions.
F.LE.A.4
F.BF.B.4.B
Develop and use the power property of logarithms to write equivalent expressions.
F.LE.A.4
Solve equations with logarithms.
F.LE.A.4
A.SSE.A.1.B
Use logarithms to solve exponential modeling problems (Part I).
F.LE.A.4
A.SSE.A.1.B
Use logarithms to solve exponential modeling problems (Part II).
Key: Major Cluster Supporting Cluster Additional Cluster
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