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# Unit: Module 3: Exponential and logarithmic functions

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### About this unit

"In this module, students synthesize and generalize what they have learned about a variety of function families. They extend the domain of exponential functions to the entire real line (N-RN.A.1) and then extend their work with these functions to include solving exponential equations with logarithms (F-LE.A.4). They explore (with appropriate tools) the effects of transformations on graphs of exponential and logarithmic functions. They notice that the transformations on a graph of a logarithmic function relate to the logarithmic properties (F-BF.B.3). Students identify appropriate types of functions to model a situation. They adjust parameters to improve the model, and they compare models by analyzing appropriateness of fit and making judgments about the domain over which a model is a good fit. The description of modeling as, “the process of choosing and using mathematics and statistics to analyze empirical situations, to understand them better, and to make decisions,” is at the heart of this module. In particular, through repeated opportunities in working through the modeling cycle (see page 61 of the CCLS), students acquire the insight that the same mathematical or statistical structure can sometimes model seemingly different situations." Eureka Math/EngageNY (c) 2015 GreatMinds.org### Learn

### Practice

- Multiply & divide powers (integer exponents)Get 5 of 7 questions to level up!
- Powers of products & quotients (integer exponents)Get 3 of 4 questions to level up!

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- Scientific notationGet 5 of 7 questions to level up!
- Multiplying & dividing in scientific notationGet 3 of 4 questions to level up!
- Adding & subtracting in scientific notationGet 3 of 4 questions to level up!
- Scientific notation word problemsGet 3 of 4 questions to level up!

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- Unit-fraction exponentsGet 3 of 4 questions to level up!
- Fractional exponentsGet 3 of 4 questions to level up!
- Rational exponents challengeGet 3 of 4 questions to level up!
- Properties of exponents intro (rational exponents)Get 3 of 4 questions to level up!
- Properties of exponents (rational exponents)Get 3 of 4 questions to level up!

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### Practice

- Solve exponential equations using exponent propertiesGet 3 of 4 questions to level up!
- Evaluate logarithmsGet 3 of 4 questions to level up!
- Evaluate logarithms (advanced)Get 3 of 4 questions to level up!

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### Practice

- Use the properties of logarithmsGet 3 of 4 questions to level up!

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### Practice

- Evaluate logarithms: change of base ruleGet 3 of 4 questions to level up!
- Use the logarithm change of base ruleGet 3 of 4 questions to level up!

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### Practice

- Solve exponential equations using logarithms: base-10 and base-eGet 3 of 4 questions to level up!
- Solve exponential equations using logarithms: base-2 and other basesGet 3 of 4 questions to level up!

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### Practice

- Approximating square rootsGet 3 of 4 questions to level up!
- Comparing irrational numbersGet 5 of 7 questions to level up!
- Comparing irrational numbers with a calculatorGet 5 of 7 questions to level up!
- Rational vs. irrational expressionsGet 3 of 4 questions to level up!

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### Practice

- Relationship between exponentials & logarithmsGet 3 of 4 questions to level up!
- Graphs of exponential functionsGet 3 of 4 questions to level up!
- Graphs of logarithmic functionsGet 3 of 4 questions to level up!

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### Learn

### Practice

- Solve exponential equations using exponent properties (advanced)Get 3 of 4 questions to level up!
- Exponential model word problemsGet 3 of 4 questions to level up!

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### Practice

- Interpret change in exponential modelsGet 3 of 4 questions to level up!
- Interpret time in exponential modelsGet 3 of 4 questions to level up!
- Construct exponential modelsGet 3 of 4 questions to level up!
- Interpret change in exponential models: with manipulationGet 3 of 4 questions to level up!
- Interpret change in exponential models: changing unitsGet 3 of 4 questions to level up!

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### Practice

- Summation notation introGet 3 of 4 questions to level up!
- Finite geometric seriesGet 3 of 4 questions to level up!
- Finite geometric series word problemsGet 3 of 4 questions to level up!

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### Practice

- Arithmetic seriesGet 3 of 4 questions to level up!

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