Unit 5: Exponential and Logarithmic Functions
Lesson Video
Focus Standards
Learning Focus
Additional Resources
Lesson 1: Log Logic
Develop Understanding
Introduces the formal definition of logarithms and provides opportunities to make sense of the notation. Introduces properties of logarithms and familiarizes the pattern of logarithmic expressions through evaluating and comparing various logarithms.
Find exact and estimated values of logarithms.
Make conjectures about logarithm properties.
What is a logarithm?
How can we tell if one log expression is bigger than another?
How can we estimate log values?
How do logs relate to exponents?
Lesson 2: Log In, Log Out
Develop Understanding
Applies understanding of transformation to exponential functions. Compares features of exponential functions with bases greater than and bases between and . Uses understanding of a logarithm as the inverse of an exponential to develop the graph of a logarithmic function.
Identify and explain common features of the graphs of exponential functions.
Identify and explain common features of the graphs of logarithmic functions.
Transform the graph of an exponential or logarithmic function.
What are the features of the graphs of logarithmic functions?
How can we use the features of the parent function to transform exponential and logarithmic functions?
How does transforming the graphs of exponential and logarithmic functions compare to transforming quadratic functions?
Lesson 3: Be the Lizard Wizard
Develop Understanding
Models the growth of an invasive species with equivalent exponential functions that reflect different time intervals. Extends understanding of rational exponents to interpret algebraic expressions in context.
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Model the growth of an invasive species.
Explain why exponential functions are good models for unchecked population growth.
Relate expressions with rational exponents to the growth of a population.
How can we describe the growth of an invasive species?
Which is a more efficient way to change the form of a radical expression: using radicals or using exponents?
How do the properties of exponents help explain equivalent forms of exponential functions?
Lesson 4: Common Sense
Solidify Understanding
Develops ideas about solving logarithmic equations and exponential equations that require the use of logarithms. Practices reading graphs of logarithms to find specific values and writing equations of logarithmic functions.
Use logarithms to solve exponential equations.
Solve systems of equations that contain exponential functions.
How can we use logarithms and algebraic reasoning to help us solve exponential equations?
Lesson 5: Money Matters
Develop Understanding
Models compound interest with exponential functions and uses logarithms to solve exponential equations in any base.
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Model the growth of a savings account earning compound interest.
Solve exponential equations using logarithms.
What does the structure of an equation tell us about the context that it models and how to solve it?