Algebra 2

Grade: HS Subject: Alg 2 (worksheets taken from Pearson)

Topic: Exponential & Logarithmic Functions

What Your Student is Learning: Representations of exponential and logarithmic models (word problems, functions, tables, graphs), Transforming Exponential and Logarithmic Functions, Properties of Exponential Functions, Logarithmic functions as an inverse of exponential functions, properties of logarithms, solving exponential and logarithmic equations, introduction to the natural logarithm

Background and Context for Parents: In middle school and Algebra 1, students both created and analyzed the different representations and structure of linear functions. They were introduced to the concept of non-linear funcitons, but just as a way to differentiate. In Algebra 2, they dive deep into non-linear functions, including exponential and logarithmic functions. In this unit, students will study how exponential functions behave. If you have a pattern that is repeated by the same number everytime, you can represent repeated multiplication with a function in the form of y = abx, where b is a number other than 1. The result is that these functions change over time by the same percentage, where we see a really slow start and then very rapid growth (like an epidemic or a viral video), or the opposite situation (decay, like the half life of medicine). Students need to work to become efficient at using all of the different representations of an exponential function in sections 7-1 and 7-2. Students are then introduced to the concept of logarithms. A logarithm is the power to which a number must be raised in order to get some other number. For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2. Logarithms are used when measuring sound (decibels) or earthquakes (Richter scale). Students then explore the relationship between the two functions. They need to use exponents to solve logarithmic equations, and logarithms to solve exponential equations. They need to understand how exponential functions and logarithmic functions are related (they are the inverse of each other!) and therefore they can be useful in solving equations involving each of them.

Ways to support your student: ● Before giving your student the answer to their question or specific help, ask them “What have you

tried so far?, What do you know?, What might be a next step? ● After your student has solved it, and before you tell them it’s correct or not, have them explain to you

how they got their solution and if they think their answer makes sense. ● Play the log race as practice! (https://www.bigideasmath.com/uploads/games/hs/elf_log_race_hs.pdf) ● Ask your student whether they would rather have $1 million dollars or 1 penny doubled each day for a

month. See what they say and then do the math together. Are you surprised by the results? (This is

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exponential growth!) ● Look at the graphs and data from the recent Coronavirus outbreak. Is it trending like an exponential

model? Why or why not? Discuss it with your student.

Online Resources for Students: https://www.nytimes.com/2020/02/18/learning/whats-going-on-in-this-graph-coronavirus-outbreak.html https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-vs-linear-growth/v/exponential-growth-functions https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:log-intro/v/logarithms

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Answer Keys

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