Students revisit exponential functions, including geometric sequences and series, and learn to manipulate logarithmic expressions and equations to solve problems involving exponential modeling.
Math
Unit 5
11th Grade
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.
Pacing: 18 instructional days (16 lessons, 1 flex day, 1 assessment day)
This assessment accompanies Unit 5 and should be given on the suggested assessment day or after completing the unit.
Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
Unit-Specific Intellectual Prep
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 |
Topic A: Modeling with and Interpreting Exponential Functions
Topic B: Definition and Meaning of Logarithms
Key
Major Cluster
Supporting Cluster
Additional Cluster
CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.
CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4 — Model with mathematics.
CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.
CCSS.MATH.PRACTICE.MP6 — Attend to precision.
CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.
CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.
Unit 4
Rational and Radical Functions
Unit 6
Unit Circle and Trigonometric Functions