Overview
| Site: | Clare-Gladwin RESD |
| Course: | Michigan Algebra II KHauck |
| Book: | Overview |
| Printed by: | Guest user |
| Date: | Sunday, May 19, 2024, 10:05 PM |
Description
Overview
Overview
The purpose of this unit is to examine the inverse relationship between exponential and logarithmic functions. You will also explore how exponential and logarithmic functions are used to solve a wide variety of problems.Common applications of exponential functions are compound interest and depreciating value. Logarithmic functions are used for half-life problems, logarithmic scales such as the Richter scale, and pH problems in chemistry.
In this unit, you will learn to identify and use exponential growth and decay functions. You will learn the definition of a logarithm and its connection to exponential functions, and use this inverse relationship to manipulate exponential and logarithmic functions to solve real world problems. You will also learn to graph exponential and logarithmic functions.
Expectations
MI Alg2 High School Content Expectations
Addressed Within the Exponential and Logarithmic Functions Unit
Addressed Within the Exponential and Logarithmic Functions Unit
L1.2.1 Use mathematical symbols to represent quantitative relationships and situations.
L2.1.3 Explain the exponential relationship between a number and its base 10 logarithm, and use it to relate rules of logarithms to those of exponents in expressions involving numbers.
L2.3.2 Describe and interpret logarithmic relationships in such contexts as the Richter scale, the pH scale, or decibel measurements; solve applied problems.
A1.1.1 Give a verbal description of an expression that is presented in symbolic form, write an algebraic expression from a verbal description, and evaluate expressions given values of the variables.
A1.1.6 Transform exponential and logarithmic expressions into equivalent forms using the properties of exponents and logarithms, including the inverse relationship between exponents and logarithms.
A1.2.2
A1.2.7 Solve exponential and logarithmic equations and justify steps in the solution.
A1.2.8 Solve an equation involving several variables (with numerical or letter coefficients) for a designated variable, and justify steps in the solution.
A1.2.9 Know common formulas and apply appropriately in contextual situations.
A2.1.3 Represent functions in symbols, graphs, tables, diagrams, or words, and translate among representations.
A2.1.7 Identify and interpret the key features of a function from its graph or its formula(s).
A2.2.3 Recognize whether a function (given in tabular or graphical form) has an inverse, and recognize simple inverse pairs.
A2.3.1 Identify a function as a member of a family of functions based on its symbolic or graphical representations; recognize that different families of functions have different asymptotic behavior.
A2.3.3 Write the general symbolic forms that characterize each family of functions.
A2.4.1 Identify the family of functions best suited for modeling a given real-world situation.
A2.4.2 Adapt the general symbolic form of a function to one that fits the
specifications of a given situation by using the information to replace arbitrary constants with numbers.
A2.4.3 Using the adapted general symbolic form, draw reasonable conclusions about the situation being modeled.
A3.2.2 Interpret the symbolic forms and recognize the graphs of exponential and logarithmic functions.A3.2.3 Apply properties of exponential and logarithmic functions.