# Exponential & logarithmic functions

## Exponent properties review

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Multiplying & dividing powers (integer exponents)Powers of products & quotients (integer exponents)

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Intro to square rootsUnderstanding square rootsIntro to cube rootsSquare root of decimal5th roots
Practice
7 questions
7 questions
3 questions

## Rational exponents intro

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Intro to rational exponentsRewriting roots as rational exponentsExponential equation with rational answer

## Properties of exponents (rational exponents)

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Rewriting quotient of powers (rational exponents)Rewriting mixed radical and exponential expressions

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Evaluating fractional exponentsEvaluating fractional exponents: negative unit-fractionEvaluating fractional exponents: fractional baseEvaluating quotient of fractional exponentsEvaluating mixed radicals and exponents

## Simplifying square roots

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Simplifying square rootsSimplifying square roots (variables)Simplifying square-root expressionsSimplifying square roots review

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Simplifying higher-index rootsSimplifying cube root expressionsSimplifying cube root expressions (two variables)Simplifying higher-index root expressions

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Simplifying square-root expressions: no variablesSimplifying square roots of fractionsSimplifying rational exponent expressions: mixed exponents and radicalsSimplifying square-root expressions: no variables (advanced)Intro to rationalizing the denominatorWorked example: rationalizing the denominatorSimplifying radical expressions (addition)Simplifying radical expressions (subtraction)Simplifying radical expressions: two variablesSimplifying radical expressions: three variablesSimplifying hairy expression with fractional exponents

## Exponential vs. linear growth

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Intro to exponential functionsExponential vs. linear growthExponential vs. linear models: verbalExponential vs. linear models: table

## Exponential expressions

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Exponential expressions word problems (numerical)Initial value & common ratio of exponential functionsExponential expressions word problems (algebraic)Interpreting exponential expression word problem
Practice

## Graphs of exponential growth

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Exponential function graphGraphs of exponential growth
Practice

## Exponential vs. linear growth over time

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Exponential vs. linear growth over time

## Exponential decay

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Exponential decay introGraphing exponential growth & decayExponential growth & decay word problems

## Exponential functions from tables & graphs

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Writing exponential functionsWriting exponential functions from tablesWriting exponential functions from graphsAnalyzing tables of exponential functionsAnalyzing graphs of exponential functionsAnalyzing graphs of exponential functions: negative initial valueModeling with basic exponential functions word problem

## Equivalent forms of exponential expressions

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Rewriting exponential expressions as A⋅BᵗEquivalent forms of exponential expressions

## Solving exponential equations using properties of exponents

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Solving exponential equations using exponent propertiesSolving exponential equations using exponent properties (advanced)
Practice

## Introduction to rate of exponential growth and decay

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Exponential growth & decay word problems

## Interpreting the rate of change of exponential models (Algebra 2 level)

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Interpreting change in exponential modelsInterpreting time in exponential models

## Constructing exponential models according to rate of change (Algebra 2 level)

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Constructing exponential modelsConstructing exponential models: half lifeConstructing exponential models: percent changeConstructing exponential models (old example)
Practice

## Advanced interpretation of exponential models (Algebra 2 level)

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Interpreting change in exponential models: with manipulationInterpreting change in exponential models: changing unitsStructure in exponential expression
Practice

## Distinguishing between linear and exponential growth (Algebra 2 level)

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Linear vs. exponential growth: from dataLinear vs. exponential growth: from data (example 2)Comparing growth of exponential & quadratic models

## Introduction to logarithms (Algebra 2 level)

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Intro to logarithmsIntro to LogarithmsEvaluating logarithms (advanced)Relationship between exponentials & logarithmsRelationship between exponentials & logarithms: graphsRelationship between exponentials & logarithms: tables

## The constant e and the natural logarithm (Algebra 2 level)

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𝑒 and compound interest𝑒 as a limitEvaluating natural logarithm with calculator

## Properties of logarithms (Algebra 2 level)

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Intro to logarithm properties (1 of 2)Intro to logarithm properties (2 of 2)Intro to logarithm propertiesUsing the logarithmic product ruleUsing the logarithmic power ruleUsing the properties of logarithms: multiple stepsProof of the logarithm product ruleProof of the logarithm quotient and power rulesJustifying the logarithm properties

## The change of base formula for logarithms (Algebra 2 level)

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Evaluating logarithms: change of base ruleLogarithm change of base rule introUsing the logarithm change of base ruleProof of the logarithm change of base ruleLogarithm properties review

## Logarithmic equations (Algebra 2 level)

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Logarithmic equations: variable in the argumentLogarithmic equations: variable in the base

## Solving exponential equations with logarithms (Algebra 2 level)

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Solving exponential equations using logarithms: base-10Solving exponential equations using logarithmsSolving exponential equations using logarithms: base-2

## Solving exponential models (Algebra 2 level)

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Exponential model word problem: medication dissolveExponential model word problem: bacteria growth

## Graphs of exponential functions (Algebra 2 level)

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Transforming exponential graphsTransforming exponential graphs (example 2)Graphing exponential functionsExponential function graphGraphs of exponential functions (old example)

## Graphs of logarithmic functions (Algebra 2 level)

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Graphical relationship between 2ˣ and log₂(x)Shape of a logarithmic parent graphGraphs of logarithmic functionsVertical asymptote of natural log

## Logarithmic scale (Algebra 2 level)

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Logarithmic scale (with Vi Hart)Logarithmic scaleRichter scaleBenford's law (with Vi Hart, 1 of 2)Benford's law (with Vi Hart, 2 of 2)

#### Unit test

Test your understanding of Exponential & logarithmic functions with these 42 questions.